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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 70560.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.c1 | 70560bc4 | \([0, 0, 0, -165963, 26017922]\) | \(11512557512/2835\) | \(124491239953920\) | \([2]\) | \(393216\) | \(1.6925\) | |
| 70560.c2 | 70560bc3 | \([0, 0, 0, -77763, -8124298]\) | \(1184287112/36015\) | \(1581499826081280\) | \([2]\) | \(393216\) | \(1.6925\) | |
| 70560.c3 | 70560bc1 | \([0, 0, 0, -11613, 303212]\) | \(31554496/11025\) | \(60516574977600\) | \([2, 2]\) | \(196608\) | \(1.3460\) | \(\Gamma_0(N)\)-optimal |
| 70560.c4 | 70560bc2 | \([0, 0, 0, 34692, 2118368]\) | \(13144256/13125\) | \(-4610786664960000\) | \([2]\) | \(393216\) | \(1.6925\) |
Rank
sage: E.rank()
The elliptic curves in class 70560.c have rank \(1\).
Complex multiplication
The elliptic curves in class 70560.c do not have complex multiplication.Modular form 70560.2.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.
