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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 5184.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5184.ba1 | 5184r2 | \([0, 0, 0, -756, -7992]\) | \(790272\) | \(60466176\) | \([]\) | \(1728\) | \(0.40153\) | |
| 5184.ba2 | 5184r1 | \([0, 0, 0, -36, 72]\) | \(6912\) | \(746496\) | \([]\) | \(576\) | \(-0.14778\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5184.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 5184.ba do not have complex multiplication.Modular form 5184.2.a.ba
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.
