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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 10830.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.ba1 | 10830bd2 | \([1, 0, 0, -721466, 235308900]\) | \(882774443450089/2166000000\) | \(101901378246000000\) | \([2]\) | \(241920\) | \(2.1417\) | |
10830.ba2 | 10830bd1 | \([1, 0, 0, -28346, 6440676]\) | \(-53540005609/350208000\) | \(-16475843893248000\) | \([2]\) | \(120960\) | \(1.7952\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10830.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 10830.ba do not have complex multiplication.Modular form 10830.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.