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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 36300.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36300.ba1 | 36300m2 | \([0, -1, 0, -133355108, 592782218712]\) | \(-2527934627152/9\) | \(-933747285636000000\) | \([]\) | \(3592512\) | \(3.0900\) | |
36300.ba2 | 36300m1 | \([0, -1, 0, -1586108, 875870712]\) | \(-4253392/729\) | \(-75633530136516000000\) | \([]\) | \(1197504\) | \(2.5407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36300.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 36300.ba do not have complex multiplication.Modular form 36300.2.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.