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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 435120v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435120.v2 | 435120v1 | \([0, -1, 0, -15451, 689410]\) | \(216727177216/17968125\) | \(33822911010000\) | \([2]\) | \(1277952\) | \(1.3382\) | \(\Gamma_0(N)\)-optimal* |
435120.v1 | 435120v2 | \([0, -1, 0, -242076, 45923760]\) | \(52089777754576/407925\) | \(12285943891200\) | \([2]\) | \(2555904\) | \(1.6848\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435120v have rank \(2\).
Complex multiplication
The elliptic curves in class 435120v do not have complex multiplication.Modular form 435120.2.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.