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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 25050ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25050.w1 | 25050ba1 | \([1, 0, 0, -388, 6392]\) | \(-16539745/36072\) | \(-14090625000\) | \([3]\) | \(29520\) | \(0.63619\) | \(\Gamma_0(N)\)-optimal |
25050.w2 | 25050ba2 | \([1, 0, 0, 3362, -139858]\) | \(10758425855/27944778\) | \(-10915928906250\) | \([]\) | \(88560\) | \(1.1855\) |
Rank
sage: E.rank()
The elliptic curves in class 25050ba have rank \(0\).
Complex multiplication
The elliptic curves in class 25050ba do not have complex multiplication.Modular form 25050.2.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.