Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2940.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2940.j1 | 2940l2 | \([0, 1, 0, -1500, -14652]\) | \(4253563312/1476225\) | \(129624364800\) | \([2]\) | \(3840\) | \(0.83395\) | |
| 2940.j2 | 2940l1 | \([0, 1, 0, -625, 5648]\) | \(4927700992/151875\) | \(833490000\) | \([2]\) | \(1920\) | \(0.48738\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2940.j have rank \(1\).
Complex multiplication
The elliptic curves in class 2940.j do not have complex multiplication.Modular form 2940.2.a.j
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.
