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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 310464.dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.dm1 | 310464dm1 | \([0, 0, 0, -104076, 12913264]\) | \(598885164/539\) | \(112207193505792\) | \([2]\) | \(1376256\) | \(1.6204\) | \(\Gamma_0(N)\)-optimal |
310464.dm2 | 310464dm2 | \([0, 0, 0, -80556, 18906160]\) | \(-138853062/290521\) | \(-120959354599243776\) | \([2]\) | \(2752512\) | \(1.9669\) |
Rank
sage: E.rank()
The elliptic curves in class 310464.dm have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.dm do not have complex multiplication.Modular form 310464.2.a.dm
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.