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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 87360.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.f1 | 87360d4 | \([0, -1, 0, -44801, 3605985]\) | \(303491543846408/5620680975\) | \(184178474188800\) | \([2]\) | \(393216\) | \(1.5316\) | |
| 87360.f2 | 87360d2 | \([0, -1, 0, -5801, -83415]\) | \(5271657955264/2282450625\) | \(9348917760000\) | \([2, 2]\) | \(196608\) | \(1.1851\) | |
| 87360.f3 | 87360d1 | \([0, -1, 0, -4956, -132594]\) | \(210390079802176/104961675\) | \(6717547200\) | \([2]\) | \(98304\) | \(0.83850\) | \(\Gamma_0(N)\)-optimal |
| 87360.f4 | 87360d3 | \([0, -1, 0, 19679, -638879]\) | \(25719397179832/20155078125\) | \(-660441600000000\) | \([2]\) | \(393216\) | \(1.5316\) |
Rank
sage: E.rank()
The elliptic curves in class 87360.f have rank \(1\).
Complex multiplication
The elliptic curves in class 87360.f do not have complex multiplication.Modular form 87360.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
