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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4830x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.w1 | 4830x1 | \([1, 1, 1, -5165, -144925]\) | \(15238420194810961/12619514880\) | \(12619514880\) | \([2]\) | \(6720\) | \(0.86658\) | \(\Gamma_0(N)\)-optimal |
4830.w2 | 4830x2 | \([1, 1, 1, -4045, -208093]\) | \(-7319577278195281/14169067365600\) | \(-14169067365600\) | \([2]\) | \(13440\) | \(1.2132\) |
Rank
sage: E.rank()
The elliptic curves in class 4830x have rank \(0\).
Complex multiplication
The elliptic curves in class 4830x do not have complex multiplication.Modular form 4830.2.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.