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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 19350.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19350.cv1 | 19350cj2 | \([1, -1, 1, -37299605, 87689980397]\) | \(503835593418244309249/898614000000\) | \(10235775093750000000\) | \([2]\) | \(1935360\) | \(2.9060\) | |
19350.cv2 | 19350cj1 | \([1, -1, 1, -2307605, 1399708397]\) | \(-119305480789133569/5200091136000\) | \(-59232288096000000000\) | \([2]\) | \(967680\) | \(2.5594\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19350.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 19350.cv do not have complex multiplication.Modular form 19350.2.a.cv
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 LMFDB 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 LMFDB labels.