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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 25872.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25872.q1 | 25872bg2 | \([0, -1, 0, -56656168, 164160565360]\) | \(121681065322255375/12702096\) | \(2099508797686874112\) | \([2]\) | \(1376256\) | \(2.9446\) | |
25872.q2 | 25872bg1 | \([0, -1, 0, -3532328, 2579093616]\) | \(-29489309167375/303595776\) | \(-50180852250886275072\) | \([2]\) | \(688128\) | \(2.5980\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25872.q have rank \(1\).
Complex multiplication
The elliptic curves in class 25872.q do not have complex multiplication.Modular form 25872.2.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.