Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 88872c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88872.b4 | 88872c1 | \([0, -1, 0, -3879, -602100]\) | \(-2725888/64827\) | \(-153547561219248\) | \([2]\) | \(295680\) | \(1.4028\) | \(\Gamma_0(N)\)-optimal |
| 88872.b3 | 88872c2 | \([0, -1, 0, -133484, -18643116]\) | \(6940769488/35721\) | \(1353725437688064\) | \([2, 2]\) | \(591360\) | \(1.7494\) | |
| 88872.b2 | 88872c3 | \([0, -1, 0, -207544, 4433980]\) | \(6522128932/3720087\) | \(563923339471199232\) | \([2]\) | \(1182720\) | \(2.0959\) | |
| 88872.b1 | 88872c4 | \([0, -1, 0, -2133104, -1198418916]\) | \(7080974546692/189\) | \(28650273813504\) | \([2]\) | \(1182720\) | \(2.0959\) |
Rank
sage: E.rank()
The elliptic curves in class 88872c have rank \(0\).
Complex multiplication
The elliptic curves in class 88872c do not have complex multiplication.Modular form 88872.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
