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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 25150k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25150.m2 | 25150k1 | \([1, -1, 1, 195, 197]\) | \(52734375/32192\) | \(-503000000\) | \([2]\) | \(9072\) | \(0.35887\) | \(\Gamma_0(N)\)-optimal |
25150.m1 | 25150k2 | \([1, -1, 1, -805, 2197]\) | \(3687953625/2024072\) | \(31626125000\) | \([2]\) | \(18144\) | \(0.70544\) |
Rank
sage: E.rank()
The elliptic curves in class 25150k have rank \(0\).
Complex multiplication
The elliptic curves in class 25150k do not have complex multiplication.Modular form 25150.2.a.k
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.