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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 121968ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121968.bb2 | 121968ba1 | \([0, 0, 0, 429, 6050]\) | \(8788/21\) | \(-20865309696\) | \([2]\) | \(61440\) | \(0.66406\) | \(\Gamma_0(N)\)-optimal |
121968.bb1 | 121968ba2 | \([0, 0, 0, -3531, 67034]\) | \(2450086/441\) | \(876343007232\) | \([2]\) | \(122880\) | \(1.0106\) |
Rank
sage: E.rank()
The elliptic curves in class 121968ba have rank \(2\).
Complex multiplication
The elliptic curves in class 121968ba do not have complex multiplication.Modular form 121968.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.