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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 25872.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25872.v1 | 25872br2 | \([0, -1, 0, -82728, -8689680]\) | \(129938649625/7072758\) | \(3408293502738432\) | \([2]\) | \(147456\) | \(1.7363\) | |
25872.v2 | 25872br1 | \([0, -1, 0, 3512, -548624]\) | \(9938375/274428\) | \(-132244192346112\) | \([2]\) | \(73728\) | \(1.3897\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25872.v have rank \(0\).
Complex multiplication
The elliptic curves in class 25872.v do not have complex multiplication.Modular form 25872.2.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 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.