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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 19074.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19074.j1 | 19074h2 | \([1, 0, 1, -13738152402, -619785496609820]\) | \(2418067440128989194388361/8359273562112\) | \(991308500788375114481664\) | \([2]\) | \(27783168\) | \(4.2482\) | |
| 19074.j2 | 19074h1 | \([1, 0, 1, -859017682, -9675126653980]\) | \(591139158854005457801/1097587482427392\) | \(130160568810752720265805824\) | \([2]\) | \(13891584\) | \(3.9016\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19074.j have rank \(0\).
Complex multiplication
The elliptic curves in class 19074.j do not have complex multiplication.Modular form 19074.2.a.j
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.
