Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 388416.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.t1 | 388416t2 | \([0, -1, 0, -17876769, 27296662209]\) | \(20324066489/1411788\) | \(43888395153295706947584\) | \([2]\) | \(50135040\) | \(3.0925\) | |
| 388416.t2 | 388416t1 | \([0, -1, 0, 989151, 1846536129]\) | \(3442951/49392\) | \(-1535454057841249222656\) | \([2]\) | \(25067520\) | \(2.7459\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388416.t have rank \(0\).
Complex multiplication
The elliptic curves in class 388416.t do not have complex multiplication.Modular form 388416.2.a.t
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.
