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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 493680cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.cv1 | 493680cv1 | \([0, -1, 0, -198480, 34718400]\) | \(-119168121961/2524500\) | \(-18318564329472000\) | \([]\) | \(4147200\) | \(1.9110\) | \(\Gamma_0(N)\)-optimal |
493680.cv2 | 493680cv2 | \([0, -1, 0, 817920, 155873280]\) | \(8339492177639/6277634880\) | \(-45552488962652897280\) | \([]\) | \(12441600\) | \(2.4603\) |
Rank
sage: E.rank()
The elliptic curves in class 493680cv have rank \(1\).
Complex multiplication
The elliptic curves in class 493680cv do not have complex multiplication.Modular form 493680.2.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 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.