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SageMath
E = EllipticCurve("gp1")
E.isogeny_class()
Elliptic curves in class 212160.gp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.gp1 | 212160em1 | \([0, 1, 0, -878072325, 9859480705035]\) | \(73116370343393432970075848704/1300080752662933887626565\) | \(1331282690726844300929602560\) | \([2]\) | \(106168320\) | \(4.0006\) | \(\Gamma_0(N)\)-optimal |
| 212160.gp2 | 212160em2 | \([0, 1, 0, -17137905, 28348391748303]\) | \(-33976371095524781961424/21189486433734191630763225\) | \(-347168545730300995678424678400\) | \([2]\) | \(212336640\) | \(4.3472\) |
Rank
sage: E.rank()
The elliptic curves in class 212160.gp have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.gp do not have complex multiplication.Modular form 212160.2.a.gp
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.
