Show commands:
SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 397800.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.cg1 | 397800cg1 | \([0, 0, 0, -63228675, -193227039250]\) | \(2396726313900986596/4154072495625\) | \(48453101588970000000000\) | \([2]\) | \(35389440\) | \(3.2468\) | \(\Gamma_0(N)\)-optimal |
| 397800.cg2 | 397800cg2 | \([0, 0, 0, -43455675, -316274418250]\) | \(-389032340685029858/1627263833203125\) | \(-37960810700962500000000000\) | \([2]\) | \(70778880\) | \(3.5934\) |
Rank
sage: E.rank()
The elliptic curves in class 397800.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.cg do not have complex multiplication.Modular form 397800.2.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 LMFDB 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 LMFDB labels.
