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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 490e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490.g2 | 490e1 | \([1, 0, 0, -1, -15]\) | \(-49/40\) | \(-96040\) | \([3]\) | \(60\) | \(-0.36492\) | \(\Gamma_0(N)\)-optimal |
490.g1 | 490e2 | \([1, 0, 0, -491, -4229]\) | \(-5452947409/250\) | \(-600250\) | \([]\) | \(180\) | \(0.18439\) |
Rank
sage: E.rank()
The elliptic curves in class 490e have rank \(0\).
Complex multiplication
The elliptic curves in class 490e do not have complex multiplication.Modular form 490.2.a.e
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.