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SageMath
E = EllipticCurve("gg1")
E.isogeny_class()
Elliptic curves in class 176400gg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.pp2 | 176400gg1 | \([0, 0, 0, -102900, 10504375]\) | \(16384/3\) | \(22063334627250000\) | \([2]\) | \(1376256\) | \(1.8546\) | \(\Gamma_0(N)\)-optimal |
| 176400.pp1 | 176400gg2 | \([0, 0, 0, -488775, -121850750]\) | \(109744/9\) | \(1059040062108000000\) | \([2]\) | \(2752512\) | \(2.2012\) |
Rank
sage: E.rank()
The elliptic curves in class 176400gg have rank \(0\).
Complex multiplication
The elliptic curves in class 176400gg do not have complex multiplication.Modular form 176400.2.a.gg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
