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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 159450.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159450.d1 | 159450t1 | \([1, 1, 0, -28609650, 58891576500]\) | \(-165745346665991446425889/10662541623558144\) | \(-166602212868096000000\) | \([]\) | \(13829760\) | \(2.9377\) | \(\Gamma_0(N)\)-optimal |
159450.d2 | 159450t2 | \([1, 1, 0, 196741350, -1692770188500]\) | \(53900230693869615719525471/110424476261224735356024\) | \(-1725382441581636489937875000\) | \([]\) | \(96808320\) | \(3.9107\) |
Rank
sage: E.rank()
The elliptic curves in class 159450.d have rank \(0\).
Complex multiplication
The elliptic curves in class 159450.d do not have complex multiplication.Modular form 159450.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.