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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 47040.ei
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47040.ei1 | 47040fz2 | \([0, 1, 0, -5161, 138935]\) | \(31554496/525\) | \(252992409600\) | \([2]\) | \(73728\) | \(0.98654\) | |
| 47040.ei2 | 47040fz1 | \([0, 1, 0, -16, 6194]\) | \(-64/2205\) | \(-16602626880\) | \([2]\) | \(36864\) | \(0.63996\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47040.ei have rank \(0\).
Complex multiplication
The elliptic curves in class 47040.ei do not have complex multiplication.Modular form 47040.2.a.ei
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
