Show commands:
SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 30960.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30960.cc1 | 30960bb2 | \([0, 0, 0, -11907, -498366]\) | \(2315685267/9245\) | \(745346396160\) | \([2]\) | \(49152\) | \(1.1349\) | |
| 30960.cc2 | 30960bb1 | \([0, 0, 0, -1107, 594]\) | \(1860867/1075\) | \(86668185600\) | \([2]\) | \(24576\) | \(0.78829\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 30960.cc do not have complex multiplication.Modular form 30960.2.a.cc
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.
