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SageMath
E = EllipticCurve("id1")
E.isogeny_class()
Elliptic curves in class 310464.id
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.id1 | 310464id1 | \([0, 0, 0, -14700, -203056]\) | \(62500/33\) | \(185485360693248\) | \([2]\) | \(737280\) | \(1.4294\) | \(\Gamma_0(N)\)-optimal |
310464.id2 | 310464id2 | \([0, 0, 0, 55860, -1586032]\) | \(1714750/1089\) | \(-12242033805754368\) | \([2]\) | \(1474560\) | \(1.7760\) |
Rank
sage: E.rank()
The elliptic curves in class 310464.id have rank \(2\).
Complex multiplication
The elliptic curves in class 310464.id do not have complex multiplication.Modular form 310464.2.a.id
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.