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SageMath
E = EllipticCurve("fa1")
E.isogeny_class()
Elliptic curves in class 172480fa
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 172480.cg2 | 172480fa1 | \([0, -1, 0, 31295, 8591297]\) | \(109902239/1100000\) | \(-33925077401600000\) | \([]\) | \(1267200\) | \(1.8530\) | \(\Gamma_0(N)\)-optimal |
| 172480.cg1 | 172480fa2 | \([0, -1, 0, -18627905, 30951471937]\) | \(-23178622194826561/1610510\) | \(-49669705823682560\) | \([]\) | \(6336000\) | \(2.6578\) |
Rank
sage: E.rank()
The elliptic curves in class 172480fa have rank \(1\).
Complex multiplication
The elliptic curves in class 172480fa do not have complex multiplication.Modular form 172480.2.a.fa
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
