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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 93600.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 93600.f1 | 93600dq4 | \([0, 0, 0, -780075, -265187250]\) | \(9001508089608/325\) | \(1895400000000\) | \([2]\) | \(786432\) | \(1.8507\) | |
| 93600.f2 | 93600dq3 | \([0, 0, 0, -78075, 1397250]\) | \(9024895368/5078125\) | \(29615625000000000\) | \([2]\) | \(786432\) | \(1.8507\) | |
| 93600.f3 | 93600dq1 | \([0, 0, 0, -48825, -4131000]\) | \(17657244864/105625\) | \(77000625000000\) | \([2, 2]\) | \(393216\) | \(1.5041\) | \(\Gamma_0(N)\)-optimal |
| 93600.f4 | 93600dq2 | \([0, 0, 0, -20700, -8856000]\) | \(-21024576/714025\) | \(-33313550400000000\) | \([2]\) | \(786432\) | \(1.8507\) |
Rank
sage: E.rank()
The elliptic curves in class 93600.f have rank \(1\).
Complex multiplication
The elliptic curves in class 93600.f do not have complex multiplication.Modular form 93600.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
