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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 169400.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169400.f1 | 169400bf2 | \([0, 1, 0, -68946808, -154575806112]\) | \(1278763167594532/375974556419\) | \(10656989778307200944000000\) | \([2]\) | \(29491200\) | \(3.5082\) | |
| 169400.f2 | 169400bf1 | \([0, 1, 0, 11578692, -16071946112]\) | \(24226243449392/29774625727\) | \(-210990262910199388000000\) | \([2]\) | \(14745600\) | \(3.1616\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 169400.f have rank \(1\).
Complex multiplication
The elliptic curves in class 169400.f do not have complex multiplication.Modular form 169400.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
