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SageMath
sage: E = EllipticCurve("ba1")
sage: E.isogeny_class()
Elliptic curves in class 15680.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
15680.ba1 | 15680cl3 | [0, -1, 0, -25741, -1654309] | [] | 41472 | |
15680.ba2 | 15680cl1 | [0, -1, 0, -261, 1891] | [] | 4608 | \(\Gamma_0(N)\)-optimal |
15680.ba3 | 15680cl2 | [0, -1, 0, 1699, -5165] | [] | 13824 |
Rank
sage: E.rank()
The elliptic curves in class 15680.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 15680.ba do not have complex multiplication.Modular form 15680.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.