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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 160080.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.a1 | 160080bp2 | \([0, -1, 0, -47581, 3759025]\) | \(46536484258668544/3286798828125\) | \(841420500000000\) | \([]\) | \(1181952\) | \(1.6112\) | |
| 160080.a2 | 160080bp1 | \([0, -1, 0, -8941, -321359]\) | \(308809465667584/1190845125\) | \(304856352000\) | \([]\) | \(393984\) | \(1.0619\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 160080.a have rank \(0\).
Complex multiplication
The elliptic curves in class 160080.a do not have complex multiplication.Modular form 160080.2.a.a
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.
