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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 60840v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60840.bk2 | 60840v1 | \([0, 0, 0, 1094613, 466251734]\) | \(40254822716/49359375\) | \(-177851384655984000000\) | \([2]\) | \(1290240\) | \(2.5717\) | \(\Gamma_0(N)\)-optimal |
60840.bk1 | 60840v2 | \([0, 0, 0, -6510387, 4480170734]\) | \(4234737878642/1247410125\) | \(8989320386052055296000\) | \([2]\) | \(2580480\) | \(2.9183\) |
Rank
sage: E.rank()
The elliptic curves in class 60840v have rank \(1\).
Complex multiplication
The elliptic curves in class 60840v do not have complex multiplication.Modular form 60840.2.a.v
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.