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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 72600bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72600.dn3 | 72600bi1 | \([0, 1, 0, -37308, 2661888]\) | \(810448/33\) | \(233846052000000\) | \([2]\) | \(245760\) | \(1.5229\) | \(\Gamma_0(N)\)-optimal |
| 72600.dn2 | 72600bi2 | \([0, 1, 0, -97808, -8228112]\) | \(3650692/1089\) | \(30867678864000000\) | \([2, 2]\) | \(491520\) | \(1.8695\) | |
| 72600.dn4 | 72600bi3 | \([0, 1, 0, 265192, -54692112]\) | \(36382894/43923\) | \(-2489992761696000000\) | \([2]\) | \(983040\) | \(2.2161\) | |
| 72600.dn1 | 72600bi4 | \([0, 1, 0, -1428808, -657756112]\) | \(5690357426/891\) | \(50510747232000000\) | \([2]\) | \(983040\) | \(2.2161\) |
Rank
sage: E.rank()
The elliptic curves in class 72600bi have rank \(1\).
Complex multiplication
The elliptic curves in class 72600bi do not have complex multiplication.Modular form 72600.2.a.bi
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
