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SageMath
E = EllipticCurve("fg1")
E.isogeny_class()
Elliptic curves in class 162240.fg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.fg1 | 162240bl3 | \([0, 1, 0, -38081, 2821599]\) | \(38614472/405\) | \(64056775311360\) | \([2]\) | \(589824\) | \(1.4658\) | |
| 162240.fg2 | 162240bl2 | \([0, 1, 0, -4281, -37881]\) | \(438976/225\) | \(4448387174400\) | \([2, 2]\) | \(294912\) | \(1.1192\) | |
| 162240.fg3 | 162240bl1 | \([0, 1, 0, -3436, -78610]\) | \(14526784/15\) | \(4633736640\) | \([2]\) | \(147456\) | \(0.77263\) | \(\Gamma_0(N)\)-optimal |
| 162240.fg4 | 162240bl4 | \([0, 1, 0, 15999, -277185]\) | \(2863288/1875\) | \(-296559144960000\) | \([2]\) | \(589824\) | \(1.4658\) |
Rank
sage: E.rank()
The elliptic curves in class 162240.fg have rank \(1\).
Complex multiplication
The elliptic curves in class 162240.fg do not have complex multiplication.Modular form 162240.2.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 LMFDB 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 LMFDB labels.
