Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 39984bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39984.be2 | 39984bc1 | \([0, -1, 0, -14373, 2522745]\) | \(-534274048000/4146834123\) | \(-2548876474706688\) | \([]\) | \(146880\) | \(1.6391\) | \(\Gamma_0(N)\)-optimal |
| 39984.be1 | 39984bc2 | \([0, -1, 0, -1919493, 1024238601]\) | \(-1272481306550272000/5865429267\) | \(-3605221291537152\) | \([]\) | \(440640\) | \(2.1884\) |
Rank
sage: E.rank()
The elliptic curves in class 39984bc have rank \(0\).
Complex multiplication
The elliptic curves in class 39984bc do not have complex multiplication.Modular form 39984.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
