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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 141570.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141570.f1 | 141570dt2 | \([1, -1, 0, -256107330, -1790442168300]\) | \(-21060895825710780845654761/3512807709348986880000\) | \(-309861255233964783697920000\) | \([]\) | \(47278080\) | \(3.8102\) | |
| 141570.f2 | 141570dt1 | \([1, -1, 0, 21402045, 9896282325]\) | \(12290700069462444495239/7592832000000000000\) | \(-669756117888000000000000\) | \([]\) | \(15759360\) | \(3.2609\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141570.f have rank \(1\).
Complex multiplication
The elliptic curves in class 141570.f do not have complex multiplication.Modular form 141570.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
