Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3380h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3380.j1 | 3380h1 | \([0, -1, 0, -47545, 4006170]\) | \(153910165504/845\) | \(65258457680\) | \([2]\) | \(8064\) | \(1.2685\) | \(\Gamma_0(N)\)-optimal |
| 3380.j2 | 3380h2 | \([0, -1, 0, -46700, 4154552]\) | \(-9115564624/714025\) | \(-882294347833600\) | \([2]\) | \(16128\) | \(1.6150\) |
Rank
sage: E.rank()
The elliptic curves in class 3380h have rank \(1\).
Complex multiplication
The elliptic curves in class 3380h do not have complex multiplication.Modular form 3380.2.a.h
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.
