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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 100793.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100793.l1 | 100793m4 | \([1, -1, 0, -537686, -151620001]\) | \(82483294977/17\) | \(3543180461513\) | \([2]\) | \(414720\) | \(1.7953\) | |
100793.l2 | 100793m2 | \([1, -1, 0, -33721, -2345568]\) | \(20346417/289\) | \(60234067845721\) | \([2, 2]\) | \(207360\) | \(1.4487\) | |
100793.l3 | 100793m3 | \([1, -1, 0, -4076, -6347643]\) | \(-35937/83521\) | \(-17407645607413369\) | \([2]\) | \(414720\) | \(1.7953\) | |
100793.l4 | 100793m1 | \([1, -1, 0, -4076, 43819]\) | \(35937/17\) | \(3543180461513\) | \([2]\) | \(103680\) | \(1.1021\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100793.l have rank \(0\).
Complex multiplication
The elliptic curves in class 100793.l do not have complex multiplication.Modular form 100793.2.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.