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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 200849f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200849.f1 | 200849f1 | \([0, -1, 1, -26267, -1907523]\) | \(-2258403328/480491\) | \(-426437531187371\) | \([]\) | \(702000\) | \(1.5286\) | \(\Gamma_0(N)\)-optimal |
200849.f2 | 200849f2 | \([0, -1, 1, 185153, 11020810]\) | \(790939860992/517504691\) | \(-459287318197267571\) | \([]\) | \(2106000\) | \(2.0779\) |
Rank
sage: E.rank()
The elliptic curves in class 200849f have rank \(1\).
Complex multiplication
The elliptic curves in class 200849f do not have complex multiplication.Modular form 200849.2.a.f
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.