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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 271950ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271950.ba2 | 271950ba1 | \([1, 1, 0, -4575, -106875]\) | \(1976656375/255744\) | \(1370628000000\) | \([2]\) | \(663552\) | \(1.0574\) | \(\Gamma_0(N)\)-optimal |
271950.ba1 | 271950ba2 | \([1, 1, 0, -18575, 859125]\) | \(132261232375/15968016\) | \(85578585750000\) | \([2]\) | \(1327104\) | \(1.4040\) |
Rank
sage: E.rank()
The elliptic curves in class 271950ba have rank \(2\).
Complex multiplication
The elliptic curves in class 271950ba do not have complex multiplication.Modular form 271950.2.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.