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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2299c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2299.c1 | 2299c1 | \([0, 1, 1, -3307, -86718]\) | \(-2258403328/480491\) | \(-851219116451\) | \([]\) | \(2880\) | \(1.0105\) | \(\Gamma_0(N)\)-optimal |
2299.c2 | 2299c2 | \([0, 1, 1, 23313, 502915]\) | \(790939860992/517504691\) | \(-916791127892651\) | \([]\) | \(8640\) | \(1.5598\) |
Rank
sage: E.rank()
The elliptic curves in class 2299c have rank \(0\).
Complex multiplication
The elliptic curves in class 2299c do not have complex multiplication.Modular form 2299.2.a.c
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.