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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 37026.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37026.z1 | 37026bl2 | \([1, -1, 1, -198221, 34016051]\) | \(666940371553/37026\) | \(47817893020194\) | \([2]\) | \(184320\) | \(1.6902\) | |
37026.z2 | 37026bl1 | \([1, -1, 1, -13091, 470495]\) | \(192100033/38148\) | \(49266920081412\) | \([2]\) | \(92160\) | \(1.3437\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37026.z have rank \(1\).
Complex multiplication
The elliptic curves in class 37026.z do not have complex multiplication.Modular form 37026.2.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 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.