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SageMath
E = EllipticCurve("nr1")
E.isogeny_class()
Elliptic curves in class 100800nr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.ju2 | 100800nr1 | \([0, 0, 0, 60, -520]\) | \(1280/7\) | \(-130636800\) | \([]\) | \(27648\) | \(0.23939\) | \(\Gamma_0(N)\)-optimal |
| 100800.ju1 | 100800nr2 | \([0, 0, 0, -3540, -81160]\) | \(-262885120/343\) | \(-6401203200\) | \([]\) | \(82944\) | \(0.78870\) |
Rank
sage: E.rank()
The elliptic curves in class 100800nr have rank \(0\).
Complex multiplication
The elliptic curves in class 100800nr do not have complex multiplication.Modular form 100800.2.a.nr
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
