Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 115920.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.bj1 | 115920bb2 | \([0, 0, 0, -10083, 386818]\) | \(75933869762/648025\) | \(967496140800\) | \([2]\) | \(221184\) | \(1.1247\) | |
| 115920.bj2 | 115920bb1 | \([0, 0, 0, -1083, -3782]\) | \(188183524/100625\) | \(75116160000\) | \([2]\) | \(110592\) | \(0.77813\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.bj have rank \(2\).
Complex multiplication
The elliptic curves in class 115920.bj do not have complex multiplication.Modular form 115920.2.a.bj
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.
