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SageMath
E = EllipticCurve("iq1")
E.isogeny_class()
Elliptic curves in class 369600.iq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.iq1 | 369600iq1 | \([0, -1, 0, -36008, 2481762]\) | \(5163364362304/352983015\) | \(352983015000000\) | \([2]\) | \(1720320\) | \(1.5398\) | \(\Gamma_0(N)\)-optimal |
| 369600.iq2 | 369600iq2 | \([0, -1, 0, 31367, 10634137]\) | \(53327207744/795685275\) | \(-50923857600000000\) | \([2]\) | \(3440640\) | \(1.8864\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.iq have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.iq do not have complex multiplication.Modular form 369600.2.a.iq
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.
