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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 310464.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.be1 | 310464be1 | \([0, 0, 0, -21116844, -37350088496]\) | \(-61279455929796531/681472\) | \(-11580941361217536\) | \([]\) | \(9953280\) | \(2.6514\) | \(\Gamma_0(N)\)-optimal |
310464.be2 | 310464be2 | \([0, 0, 0, -19987884, -41520968496]\) | \(-71285434106859/18863581528\) | \(-233693981544995415392256\) | \([]\) | \(29859840\) | \(3.2007\) |
Rank
sage: E.rank()
The elliptic curves in class 310464.be have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.be do not have complex multiplication.Modular form 310464.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.