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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 16830.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16830.d1 | 16830e1 | \([1, -1, 0, -1171410, 170143316]\) | \(9031490088862377843/4593378603827200\) | \(90411471059130777600\) | \([2]\) | \(748800\) | \(2.5217\) | \(\Gamma_0(N)\)-optimal |
16830.d2 | 16830e2 | \([1, -1, 0, 4358190, 1312558676]\) | \(465104823145335330957/307032707468861440\) | \(-6043324781109599723520\) | \([2]\) | \(1497600\) | \(2.8682\) |
Rank
sage: E.rank()
The elliptic curves in class 16830.d have rank \(1\).
Complex multiplication
The elliptic curves in class 16830.d do not have complex multiplication.Modular form 16830.2.a.d
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.