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Properties

Label 7350.f
Number of curves $6$
Conductor $7350$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("f1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 7350.f have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(13\) \( 1 - 6 T + 13 T^{2}\) 1.13.ag
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 8 T + 23 T^{2}\) 1.23.i
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 7350.f do not have complex multiplication.

Modular form 7350.2.a.f

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4 q^{11} - q^{12} + 6 q^{13} + q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 7350.f

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.f1 7350i3 \([1, 1, 0, -1646425, -813818375]\) \(268498407453697/252\) \(463242937500\) \([2]\) \(98304\) \(1.9668\)  
7350.f2 7350i5 \([1, 1, 0, -1119675, 451177875]\) \(84448510979617/933897762\) \(1716752153149031250\) \([2]\) \(196608\) \(2.3134\)  
7350.f3 7350i4 \([1, 1, 0, -127425, -6249375]\) \(124475734657/63011844\) \(115832506793062500\) \([2, 2]\) \(98304\) \(1.9668\)  
7350.f4 7350i2 \([1, 1, 0, -102925, -12741875]\) \(65597103937/63504\) \(116737220250000\) \([2, 2]\) \(49152\) \(1.6202\)  
7350.f5 7350i1 \([1, 1, 0, -4925, -295875]\) \(-7189057/16128\) \(-29647548000000\) \([2]\) \(24576\) \(1.2736\) \(\Gamma_0(N)\)-optimal
7350.f6 7350i6 \([1, 1, 0, 472825, -47666625]\) \(6359387729183/4218578658\) \(-7754868133360031250\) \([2]\) \(196608\) \(2.3134\)