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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 374850.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374850.du1 | 374850du2 | \([1, -1, 0, -29144817, -36818623409]\) | \(5956317014383/2172381210\) | \(998541116128755291093750\) | \([2]\) | \(49545216\) | \(3.3054\) | |
374850.du2 | 374850du1 | \([1, -1, 0, 5583933, -4069412159]\) | \(41890384817/39795300\) | \(-18292021260245873437500\) | \([2]\) | \(24772608\) | \(2.9589\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 374850.du have rank \(1\).
Complex multiplication
The elliptic curves in class 374850.du do not have complex multiplication.Modular form 374850.2.a.du
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 LMFDB 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 LMFDB labels.