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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3366.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3366.f1 | 3366e3 | \([1, -1, 0, -149351112, 702560755008]\) | \(505384091400037554067434625/815656731648\) | \(594613757371392\) | \([6]\) | \(276480\) | \(2.9902\) | |
| 3366.f2 | 3366e4 | \([1, -1, 0, -149349672, 702574979040]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-14801047178054396558112\) | \([6]\) | \(552960\) | \(3.3368\) | |
| 3366.f3 | 3366e1 | \([1, -1, 0, -1849032, 958443840]\) | \(959024269496848362625/11151660319506432\) | \(8129560372920188928\) | \([2]\) | \(92160\) | \(2.4409\) | \(\Gamma_0(N)\)-optimal |
| 3366.f4 | 3366e2 | \([1, -1, 0, -374472, 2443915584]\) | \(-7966267523043306625/3534510366354604032\) | \(-2576658057072506339328\) | \([2]\) | \(184320\) | \(2.7875\) |
Rank
sage: E.rank()
The elliptic curves in class 3366.f have rank \(1\).
Complex multiplication
The elliptic curves in class 3366.f do not have complex multiplication.Modular form 3366.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
