Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 33396c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33396.h2 | 33396c1 | \([0, -1, 0, -11293, 452410]\) | \(5619712000/184437\) | \(5227862338512\) | \([2]\) | \(69120\) | \(1.2138\) | \(\Gamma_0(N)\)-optimal |
| 33396.h1 | 33396c2 | \([0, -1, 0, -27628, -1135352]\) | \(5142706000/1728243\) | \(783792101714688\) | \([2]\) | \(138240\) | \(1.5604\) |
Rank
sage: E.rank()
The elliptic curves in class 33396c have rank \(1\).
Complex multiplication
The elliptic curves in class 33396c do not have complex multiplication.Modular form 33396.2.a.c
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.
