Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 90480e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90480.a2 | 90480e1 | \([0, -1, 0, -68491, 6919066]\) | \(2220805845052524544/1120803328125\) | \(17932853250000\) | \([2]\) | \(368640\) | \(1.4954\) | \(\Gamma_0(N)\)-optimal |
| 90480.a1 | 90480e2 | \([0, -1, 0, -80236, 4396240]\) | \(223150039787533264/96919189453125\) | \(24811312500000000\) | \([2]\) | \(737280\) | \(1.8420\) |
Rank
sage: E.rank()
The elliptic curves in class 90480e have rank \(0\).
Complex multiplication
The elliptic curves in class 90480e do not have complex multiplication.Modular form 90480.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
