Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 355740l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.l2 | 355740l1 | \([0, -1, 0, -3707601, 2674879110]\) | \(4927700992/151875\) | \(173717969580380610000\) | \([2]\) | \(14515200\) | \(2.6593\) | \(\Gamma_0(N)\)-optimal |
| 355740.l1 | 355740l2 | \([0, -1, 0, -8895476, -6457856040]\) | \(4253563312/1476225\) | \(27016618629140792467200\) | \([2]\) | \(29030400\) | \(3.0059\) |
Rank
sage: E.rank()
The elliptic curves in class 355740l have rank \(0\).
Complex multiplication
The elliptic curves in class 355740l do not have complex multiplication.Modular form 355740.2.a.l
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.
