Show commands:
SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 70560.cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.cn1 | 70560bv4 | \([0, 0, 0, -45008460147, -3675270815038186]\) | \(229625675762164624948320008/9568125\) | \(420157934844480000\) | \([2]\) | \(82575360\) | \(4.2822\) | |
| 70560.cn2 | 70560bv3 | \([0, 0, 0, -2822675772, -57012396271936]\) | \(7079962908642659949376/100085966990454375\) | \(35160003196130573398955520000\) | \([2]\) | \(82575360\) | \(4.2822\) | |
| 70560.cn3 | 70560bv1 | \([0, 0, 0, -2813028897, -57426100576936]\) | \(448487713888272974160064/91549016015625\) | \(502515455041730025000000\) | \([2, 2]\) | \(41287680\) | \(3.9357\) | \(\Gamma_0(N)\)-optimal |
| 70560.cn4 | 70560bv2 | \([0, 0, 0, -2803384227, -57839426767654]\) | \(-55486311952875723077768/801237030029296875\) | \(-35184123938392734375000000000\) | \([2]\) | \(82575360\) | \(4.2822\) |
Rank
sage: E.rank()
The elliptic curves in class 70560.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 70560.cn do not have complex multiplication.Modular form 70560.2.a.cn
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.
