Show commands:
SageMath
E = EllipticCurve("fw1")
E.isogeny_class()
Elliptic curves in class 356928.fw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 356928.fw1 | 356928fw1 | \([0, 1, 0, -62455921441, -6014111118265249]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-33165490490618987062666475864064\) | \([]\) | \(1137991680\) | \(4.9580\) | \(\Gamma_0(N)\)-optimal |
| 356928.fw2 | 356928fw2 | \([0, 1, 0, 176875010399, 377441846787555551]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-61897858591614152023400936009148923904\) | \([]\) | \(7965941760\) | \(5.9310\) |
Rank
sage: E.rank()
The elliptic curves in class 356928.fw have rank \(1\).
Complex multiplication
The elliptic curves in class 356928.fw do not have complex multiplication.Modular form 356928.2.a.fw
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
