Show commands:
SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 172480cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 172480.dc1 | 172480cg1 | \([0, 0, 0, -7448, -238728]\) | \(379275264/15125\) | \(1822147712000\) | \([2]\) | \(276480\) | \(1.1191\) | \(\Gamma_0(N)\)-optimal |
| 172480.dc2 | 172480cg2 | \([0, 0, 0, 3332, -872592]\) | \(2122416/171875\) | \(-331299584000000\) | \([2]\) | \(552960\) | \(1.4657\) |
Rank
sage: E.rank()
The elliptic curves in class 172480cg have rank \(1\).
Complex multiplication
The elliptic curves in class 172480cg do not have complex multiplication.Modular form 172480.2.a.cg
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.
