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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 19134.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19134.d1 | 19134b1 | \([1, -1, 0, -10299474, -12720580524]\) | \(-165745346665991446425889/10662541623558144\) | \(-7772992843573886976\) | \([]\) | \(790272\) | \(2.6823\) | \(\Gamma_0(N)\)-optimal |
| 19134.d2 | 19134b2 | \([1, -1, 0, 70826886, 365638360716]\) | \(53900230693869615719525471/110424476261224735356024\) | \(-80499443194432832074541496\) | \([]\) | \(5531904\) | \(3.6552\) |
Rank
sage: E.rank()
The elliptic curves in class 19134.d have rank \(0\).
Complex multiplication
The elliptic curves in class 19134.d do not have complex multiplication.Modular form 19134.2.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.
