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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 3380.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3380.i1 | 3380e2 | \([0, 1, 0, -290, -1975]\) | \(1000939264/15625\) | \(42250000\) | \([]\) | \(864\) | \(0.26419\) | |
| 3380.i2 | 3380e1 | \([0, 1, 0, -30, 53]\) | \(1141504/25\) | \(67600\) | \([]\) | \(288\) | \(-0.28511\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3380.i have rank \(1\).
Complex multiplication
The elliptic curves in class 3380.i do not have complex multiplication.Modular form 3380.2.a.i
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.
