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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 303600.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303600.ba1 | 303600ba2 | \([0, -1, 0, -4809508, -4056177488]\) | \(3075854342141027536/1725242578125\) | \(6900970312500000000\) | \([2]\) | \(7667712\) | \(2.5620\) | |
303600.ba2 | 303600ba1 | \([0, -1, 0, -246883, -86693738]\) | \(-6656700550752256/9159720631875\) | \(-2289930157968750000\) | \([2]\) | \(3833856\) | \(2.2154\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303600.ba have rank \(2\).
Complex multiplication
The elliptic curves in class 303600.ba do not have complex multiplication.Modular form 303600.2.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.