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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 3850x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3850.x1 | 3850x1 | \([1, -1, 1, -390, -2863]\) | \(52355598021/15092\) | \(1886500\) | \([2]\) | \(1152\) | \(0.18419\) | \(\Gamma_0(N)\)-optimal |
3850.x2 | 3850x2 | \([1, -1, 1, -340, -3663]\) | \(-34677868581/28471058\) | \(-3558882250\) | \([2]\) | \(2304\) | \(0.53076\) |
Rank
sage: E.rank()
The elliptic curves in class 3850x have rank \(0\).
Complex multiplication
The elliptic curves in class 3850x do not have complex multiplication.Modular form 3850.2.a.x
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.