Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 213444.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 213444.j1 | 213444h2 | \([0, 0, 0, -4126584, 3245036564]\) | \(-199794688/1331\) | \(-51771398906362012416\) | \([]\) | \(7776000\) | \(2.6182\) | |
| 213444.j2 | 213444h1 | \([0, 0, 0, 142296, 23739716]\) | \(8192/11\) | \(-427862800879024896\) | \([]\) | \(2592000\) | \(2.0689\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 213444.j have rank \(1\).
Complex multiplication
The elliptic curves in class 213444.j do not have complex multiplication.Modular form 213444.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
