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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 32490v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32490.q1 | 32490v1 | \([1, -1, 0, -324, 2668]\) | \(-14317849/2700\) | \(-710556300\) | \([]\) | \(20736\) | \(0.42258\) | \(\Gamma_0(N)\)-optimal |
32490.q2 | 32490v2 | \([1, -1, 0, 2241, -13235]\) | \(4728305591/3000000\) | \(-789507000000\) | \([]\) | \(62208\) | \(0.97189\) |
Rank
sage: E.rank()
The elliptic curves in class 32490v have rank \(2\).
Complex multiplication
The elliptic curves in class 32490v do not have complex multiplication.Modular form 32490.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.