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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 229840.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229840.p1 | 229840f2 | \([0, -1, 0, -17957320, 30239740400]\) | \(-32391289681150609/1228250000000\) | \(-24283251319808000000000\) | \([]\) | \(14152320\) | \(3.0654\) | |
| 229840.p2 | 229840f1 | \([0, -1, 0, 1078840, 133534192]\) | \(7023836099951/4456448000\) | \(-88106693895913472000\) | \([]\) | \(4717440\) | \(2.5161\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 229840.p have rank \(1\).
Complex multiplication
The elliptic curves in class 229840.p do not have complex multiplication.Modular form 229840.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
