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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 23826z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23826.w1 | 23826z1 | \([1, 1, 1, -74193, -6295761]\) | \(960044289625/195182592\) | \(9182536996503552\) | \([2]\) | \(161280\) | \(1.7787\) | \(\Gamma_0(N)\)-optimal |
23826.w2 | 23826z2 | \([1, 1, 1, 156847, -37439953]\) | \(9070486526375/18165704832\) | \(-854621587807396992\) | \([2]\) | \(322560\) | \(2.1252\) |
Rank
sage: E.rank()
The elliptic curves in class 23826z have rank \(1\).
Complex multiplication
The elliptic curves in class 23826z do not have complex multiplication.Modular form 23826.2.a.z
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.