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Properties

Label 18480.bl
Number of curves $6$
Conductor $18480$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bl1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 18480.bl have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1 - T\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 18480.bl do not have complex multiplication.

Modular form 18480.2.a.bl

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - q^{11} - 2 q^{13} - q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.

Elliptic curves in class 18480.bl

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.bl1 18480o5 \([0, -1, 0, -30425680, 64606578400]\) \(1520949008089505953959842/278553515625\) \(570477600000000\) \([4]\) \(589824\) \(2.6673\)  
18480.bl2 18480o3 \([0, -1, 0, -1901800, 1009735552]\) \(742879737792994384804/317817082130625\) \(325444692101760000\) \([2, 4]\) \(294912\) \(2.3207\)  
18480.bl3 18480o6 \([0, -1, 0, -1604800, 1335485152]\) \(-223180773010681046402/246754509479287425\) \(-505353235413580646400\) \([4]\) \(589824\) \(2.6673\)  
18480.bl4 18480o2 \([0, -1, 0, -137620, 10504000]\) \(1125982298608534096/467044181552025\) \(119563310477318400\) \([2, 2]\) \(147456\) \(1.9741\)  
18480.bl5 18480o1 \([0, -1, 0, -64415, -6157458]\) \(1847444944806639616/38285567941005\) \(612569087056080\) \([2]\) \(73728\) \(1.6276\) \(\Gamma_0(N)\)-optimal
18480.bl6 18480o4 \([0, -1, 0, 455280, 76434480]\) \(10191978981888338876/8372623608979245\) \(-8573566575594746880\) \([2]\) \(294912\) \(2.3207\)