Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1100.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1100.c1 | 1100e2 | \([0, 0, 0, -295, 1950]\) | \(88723728/11\) | \(352000\) | \([2]\) | \(192\) | \(0.087343\) | |
| 1100.c2 | 1100e1 | \([0, 0, 0, -20, 25]\) | \(442368/121\) | \(242000\) | \([2]\) | \(96\) | \(-0.25923\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1100.c have rank \(1\).
Complex multiplication
The elliptic curves in class 1100.c do not have complex multiplication.Modular form 1100.2.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 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.
