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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 93600di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 93600.ch3 | 93600di1 | \([0, 0, 0, -52725, 4637500]\) | \(22235451328/123201\) | \(89813529000000\) | \([2, 2]\) | \(393216\) | \(1.5202\) | \(\Gamma_0(N)\)-optimal |
| 93600.ch4 | 93600di2 | \([0, 0, 0, -23475, 9756250]\) | \(-245314376/6908733\) | \(-40291730856000000\) | \([2]\) | \(786432\) | \(1.8667\) | |
| 93600.ch2 | 93600di3 | \([0, 0, 0, -83100, -1316000]\) | \(1360251712/771147\) | \(35978634432000000\) | \([2]\) | \(786432\) | \(1.8667\) | |
| 93600.ch1 | 93600di4 | \([0, 0, 0, -842475, 297634750]\) | \(11339065490696/351\) | \(2047032000000\) | \([2]\) | \(786432\) | \(1.8667\) |
Rank
sage: E.rank()
The elliptic curves in class 93600di have rank \(1\).
Complex multiplication
The elliptic curves in class 93600di do not have complex multiplication.Modular form 93600.2.a.di
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
