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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 102966ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102966.u2 | 102966ba1 | \([1, 0, 0, -678217, -214845481]\) | \(6826561273/7074\) | \(35751381582643794\) | \([]\) | \(2608320\) | \(2.0940\) | \(\Gamma_0(N)\)-optimal |
102966.u1 | 102966ba2 | \([1, 0, 0, -2480122, 1276050716]\) | \(333822098953/53954184\) | \(272679759706555621704\) | \([]\) | \(7824960\) | \(2.6433\) |
Rank
sage: E.rank()
The elliptic curves in class 102966ba have rank \(0\).
Complex multiplication
The elliptic curves in class 102966ba do not have complex multiplication.Modular form 102966.2.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 Cremona 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 Cremona labels.