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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2652.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2652.f1 | 2652f3 | \([0, 1, 0, -4953, -19764]\) | \(840033089536000/477272151837\) | \(7636354429392\) | \([2]\) | \(4320\) | \(1.1619\) | |
| 2652.f2 | 2652f1 | \([0, 1, 0, -3153, 67104]\) | \(216727177216000/2738853\) | \(43821648\) | \([6]\) | \(1440\) | \(0.61257\) | \(\Gamma_0(N)\)-optimal |
| 2652.f3 | 2652f2 | \([0, 1, 0, -3068, 70980]\) | \(-12479332642000/1526829993\) | \(-390868478208\) | \([6]\) | \(2880\) | \(0.95915\) | |
| 2652.f4 | 2652f4 | \([0, 1, 0, 19612, -137676]\) | \(3258571509326000/1920843121977\) | \(-491735839226112\) | \([2]\) | \(8640\) | \(1.5085\) |
Rank
sage: E.rank()
The elliptic curves in class 2652.f have rank \(0\).
Complex multiplication
The elliptic curves in class 2652.f do not have complex multiplication.Modular form 2652.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
