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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 457776c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.c2 | 457776c1 | \([0, 0, 0, -421900407, 3334948281270]\) | \(68285541719739888/13451140571\) | \(1636002252788130254852352\) | \([2]\) | \(203489280\) | \(3.6454\) | \(\Gamma_0(N)\)-optimal |
457776.c1 | 457776c2 | \([0, 0, 0, -467001747, 2578192897410]\) | \(23152316479601292/7495915709689\) | \(3646779222336071497221123072\) | \([2]\) | \(406978560\) | \(3.9920\) |
Rank
sage: E.rank()
The elliptic curves in class 457776c have rank \(1\).
Complex multiplication
The elliptic curves in class 457776c do not have complex multiplication.Modular form 457776.2.a.c
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.