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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 62400.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.q1 | 62400fs2 | \([0, -1, 0, -582273, 157776417]\) | \(666276475992821/58199166792\) | \(1907070297440256000\) | \([2]\) | \(1179648\) | \(2.2482\) | |
62400.q2 | 62400fs1 | \([0, -1, 0, -569473, 165597217]\) | \(623295446073461/5458752\) | \(178872385536000\) | \([2]\) | \(589824\) | \(1.9017\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.q have rank \(1\).
Complex multiplication
The elliptic curves in class 62400.q do not have complex multiplication.Modular form 62400.2.a.q
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.