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SageMath
E = EllipticCurve("fg1")
E.isogeny_class()
Elliptic curves in class 97344fg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97344.fq3 | 97344fg1 | \([0, 0, 0, -239304, 45047288]\) | \(420616192/117\) | \(421573652517888\) | \([2]\) | \(688128\) | \(1.7880\) | \(\Gamma_0(N)\)-optimal |
| 97344.fq2 | 97344fg2 | \([0, 0, 0, -269724, 32867120]\) | \(37642192/13689\) | \(789185877513486336\) | \([2, 2]\) | \(1376256\) | \(2.1346\) | |
| 97344.fq4 | 97344fg3 | \([0, 0, 0, 825396, 232178960]\) | \(269676572/257049\) | \(-59276628133235195904\) | \([2]\) | \(2752512\) | \(2.4812\) | |
| 97344.fq1 | 97344fg4 | \([0, 0, 0, -1851564, -945975472]\) | \(3044193988/85293\) | \(19668940331874582528\) | \([2]\) | \(2752512\) | \(2.4812\) |
Rank
sage: E.rank()
The elliptic curves in class 97344fg have rank \(1\).
Complex multiplication
The elliptic curves in class 97344fg do not have complex multiplication.Modular form 97344.2.a.fg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
