Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 30800bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30800.cl2 | 30800bc1 | \([0, -1, 0, -5808, 178112]\) | \(-338608873/13552\) | \(-867328000000\) | \([2]\) | \(49152\) | \(1.0590\) | \(\Gamma_0(N)\)-optimal |
| 30800.cl1 | 30800bc2 | \([0, -1, 0, -93808, 11090112]\) | \(1426487591593/2156\) | \(137984000000\) | \([2]\) | \(98304\) | \(1.4056\) |
Rank
sage: E.rank()
The elliptic curves in class 30800bc have rank \(0\).
Complex multiplication
The elliptic curves in class 30800bc do not have complex multiplication.Modular form 30800.2.a.bc
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.
