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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 35904v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.f2 | 35904v1 | \([0, -1, 0, -769, 6913]\) | \(192100033/38148\) | \(10000269312\) | \([2]\) | \(18432\) | \(0.63514\) | \(\Gamma_0(N)\)-optimal |
| 35904.f1 | 35904v2 | \([0, -1, 0, -11649, 487809]\) | \(666940371553/37026\) | \(9706143744\) | \([2]\) | \(36864\) | \(0.98171\) |
Rank
sage: E.rank()
The elliptic curves in class 35904v have rank \(1\).
Complex multiplication
The elliptic curves in class 35904v do not have complex multiplication.Modular form 35904.2.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 Cremona 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 Cremona labels.
