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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 3520.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3520.v1 | 3520bf2 | \([0, 0, 0, -92, 304]\) | \(5256144/605\) | \(9912320\) | \([2]\) | \(512\) | \(0.074505\) | |
| 3520.v2 | 3520bf1 | \([0, 0, 0, 8, 24]\) | \(55296/275\) | \(-281600\) | \([2]\) | \(256\) | \(-0.27207\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3520.v have rank \(0\).
Complex multiplication
The elliptic curves in class 3520.v do not have complex multiplication.Modular form 3520.2.a.v
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
