Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 94192d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94192.bb2 | 94192d1 | \([0, -1, 0, -280, 99456]\) | \(-4/7\) | \(-4263693564928\) | \([2]\) | \(200704\) | \(1.1024\) | \(\Gamma_0(N)\)-optimal |
| 94192.bb1 | 94192d2 | \([0, -1, 0, -33920, 2386976]\) | \(3543122/49\) | \(59691709908992\) | \([2]\) | \(401408\) | \(1.4490\) |
Rank
sage: E.rank()
The elliptic curves in class 94192d have rank \(1\).
Complex multiplication
The elliptic curves in class 94192d do not have complex multiplication.Modular form 94192.2.a.d
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.
