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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 50400.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50400.c1 | 50400dj4 | \([0, 0, 0, -84675, -9481750]\) | \(11512557512/2835\) | \(16533720000000\) | \([2]\) | \(196608\) | \(1.5243\) | |
| 50400.c2 | 50400dj3 | \([0, 0, 0, -39675, 2960750]\) | \(1184287112/36015\) | \(210039480000000\) | \([2]\) | \(196608\) | \(1.5243\) | |
| 50400.c3 | 50400dj1 | \([0, 0, 0, -5925, -110500]\) | \(31554496/11025\) | \(8037225000000\) | \([2, 2]\) | \(98304\) | \(1.1777\) | \(\Gamma_0(N)\)-optimal |
| 50400.c4 | 50400dj2 | \([0, 0, 0, 17700, -772000]\) | \(13144256/13125\) | \(-612360000000000\) | \([2]\) | \(196608\) | \(1.5243\) |
Rank
sage: E.rank()
The elliptic curves in class 50400.c have rank \(1\).
Complex multiplication
The elliptic curves in class 50400.c do not have complex multiplication.Modular form 50400.2.a.c
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.
