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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 185130.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185130.z1 | 185130em2 | \([1, -1, 0, -12635145, -17283791475]\) | \(172735174415217961/39657600\) | \(51216520127414400\) | \([2]\) | \(6881280\) | \(2.5869\) | |
| 185130.z2 | 185130em1 | \([1, -1, 0, -786825, -271973619]\) | \(-41713327443241/639221760\) | \(-825534428127805440\) | \([2]\) | \(3440640\) | \(2.2404\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185130.z have rank \(0\).
Complex multiplication
The elliptic curves in class 185130.z do not have complex multiplication.Modular form 185130.2.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.
