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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 42350.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42350.z1 | 42350a2 | \([1, -1, 0, -24039692, 45373131216]\) | \(73877525106256274859/48189030400\) | \(1002181241600000000\) | \([2]\) | \(1935360\) | \(2.7718\) | |
| 42350.z2 | 42350a1 | \([1, -1, 0, -1511692, 700107216]\) | \(18370278334948779/460366807040\) | \(9574190940160000000\) | \([2]\) | \(967680\) | \(2.4253\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 42350.z have rank \(1\).
Complex multiplication
The elliptic curves in class 42350.z do not have complex multiplication.Modular form 42350.2.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.
