Properties

Label 97104.g
Number of curves $4$
Conductor $97104$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 97104.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97104.g1 97104bk4 \([0, -1, 0, -609784, 165115888]\) \(1246079601667529/137282971014\) \(2762634185079939072\) \([2]\) \(1536000\) \(2.2719\)  
97104.g2 97104bk2 \([0, -1, 0, -139224, -19948560]\) \(14830727012009/4704\) \(94661640192\) \([2]\) \(307200\) \(1.4672\)  
97104.g3 97104bk1 \([0, -1, 0, -8664, -312336]\) \(-3574558889/64512\) \(-1298216779776\) \([2]\) \(153600\) \(1.1207\) \(\Gamma_0(N)\)-optimal
97104.g4 97104bk3 \([0, -1, 0, 51176, 12830704]\) \(736558976791/3969746172\) \(-79885774614675456\) \([2]\) \(768000\) \(1.9254\)  

Rank

sage: E.rank()
 

The elliptic curves in class 97104.g have rank \(0\).

Complex multiplication

The elliptic curves in class 97104.g do not have complex multiplication.

Modular form 97104.2.a.g

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

Isogeny matrix

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.

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.