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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 147033.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147033.l1 | 147033l4 | \([1, -1, 0, -784356, -267177205]\) | \(82483294977/17\) | \(10998833118633\) | \([2]\) | \(967680\) | \(1.8897\) | |
147033.l2 | 147033l2 | \([1, -1, 0, -49191, -4135168]\) | \(20346417/289\) | \(186980163016761\) | \([2, 2]\) | \(483840\) | \(1.5431\) | |
147033.l3 | 147033l3 | \([1, -1, 0, -5946, -11184103]\) | \(-35937/83521\) | \(-54037267111843929\) | \([2]\) | \(967680\) | \(1.8897\) | |
147033.l4 | 147033l1 | \([1, -1, 0, -5946, 76895]\) | \(35937/17\) | \(10998833118633\) | \([2]\) | \(241920\) | \(1.1965\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 147033.l have rank \(0\).
Complex multiplication
The elliptic curves in class 147033.l do not have complex multiplication.Modular form 147033.2.a.l
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.