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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 418950.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.y1 | 418950y2 | \([1, -1, 0, -1297905948117, 568718286276311541]\) | \(1443469370754216095414793773/1214743716234132166656\) | \(203484094825246569795723948000000000\) | \([2]\) | \(8174960640\) | \(5.7027\) | \(\Gamma_0(N)\)-optimal* |
418950.y2 | 418950y1 | \([1, -1, 0, -63388188117, 12877899354071541]\) | \(-168152341439816283534893/330377478011967504384\) | \(-55342177255564930525519872000000000\) | \([2]\) | \(4087480320\) | \(5.3561\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950.y have rank \(1\).
Complex multiplication
The elliptic curves in class 418950.y do not have complex multiplication.Modular form 418950.2.a.y
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.