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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 11830.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11830.i1 | 11830m1 | \([1, -1, 0, -5728709, 4858346325]\) | \(4307585705106105969/381542350192640\) | \(1841632049790986485760\) | \([2]\) | \(887040\) | \(2.8205\) | \(\Gamma_0(N)\)-optimal |
| 11830.i2 | 11830m2 | \([1, -1, 0, 6385211, 22658540373]\) | \(5964709808210123151/49408483478681600\) | \(-238485312731251655014400\) | \([2]\) | \(1774080\) | \(3.1671\) |
Rank
sage: E.rank()
The elliptic curves in class 11830.i have rank \(1\).
Complex multiplication
The elliptic curves in class 11830.i do not have complex multiplication.Modular form 11830.2.a.i
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.
