Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 81120.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81120.bc1 | 81120bu2 | \([0, 1, 0, -576, -4536]\) | \(18821096/3645\) | \(4100129280\) | \([2]\) | \(64512\) | \(0.56153\) | |
| 81120.bc2 | 81120bu1 | \([0, 1, 0, 74, -376]\) | \(314432/675\) | \(-94910400\) | \([2]\) | \(32256\) | \(0.21496\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 81120.bc have rank \(2\).
Complex multiplication
The elliptic curves in class 81120.bc do not have complex multiplication.Modular form 81120.2.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 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.
