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Properties

Label 5880bc
Number of curves $6$
Conductor $5880$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 5880bc have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 - T\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 2 T + 11 T^{2}\) 1.11.c
\(13\) \( 1 + T + 13 T^{2}\) 1.13.b
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(19\) \( 1 + 3 T + 19 T^{2}\) 1.19.d
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 29 T^{2}\) 1.29.a
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 5880bc do not have complex multiplication.

Modular form 5880.2.a.bc

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + 4 q^{11} + 2 q^{13} - q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 5880bc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5880.z4 5880bc1 \([0, 1, 0, -36031, -2644510]\) \(2748251600896/2205\) \(4150656720\) \([2]\) \(12288\) \(1.1510\) \(\Gamma_0(N)\)-optimal
5880.z3 5880bc2 \([0, 1, 0, -36276, -2606976]\) \(175293437776/4862025\) \(146435169081600\) \([2, 2]\) \(24576\) \(1.4976\)  
5880.z2 5880bc3 \([0, 1, 0, -84296, 5690880]\) \(549871953124/200930625\) \(24206629991040000\) \([2, 2]\) \(49152\) \(1.8441\)  
5880.z5 5880bc4 \([0, 1, 0, 7824, -8498736]\) \(439608956/259416045\) \(-31252519196881920\) \([2]\) \(49152\) \(1.8441\)  
5880.z1 5880bc5 \([0, 1, 0, -1195616, 502673184]\) \(784478485879202/221484375\) \(53365586400000000\) \([2]\) \(98304\) \(2.1907\)  
5880.z6 5880bc6 \([0, 1, 0, 258704, 40539680]\) \(7947184069438/7533176175\) \(-1815082278528153600\) \([2]\) \(98304\) \(2.1907\)