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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 16245.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16245.f1 | 16245a2 | \([0, 0, 1, -56257518, 162412318188]\) | \(1590409933520896/45\) | \(557145785560005\) | \([3]\) | \(590976\) | \(2.7901\) | |
| 16245.f2 | 16245a1 | \([0, 0, 1, -699618, 219362823]\) | \(3058794496/91125\) | \(1128220215759010125\) | \([]\) | \(196992\) | \(2.2408\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16245.f have rank \(0\).
Complex multiplication
The elliptic curves in class 16245.f do not have complex multiplication.Modular form 16245.2.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.
