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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2601j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2601.g3 | 2601j1 | \([1, -1, 0, -1788, -11989]\) | \(35937/17\) | \(299136892617\) | \([2]\) | \(2304\) | \(0.89613\) | \(\Gamma_0(N)\)-optimal |
2601.g2 | 2601j2 | \([1, -1, 0, -14793, 687680]\) | \(20346417/289\) | \(5085327174489\) | \([2, 2]\) | \(4608\) | \(1.2427\) | |
2601.g1 | 2601j3 | \([1, -1, 0, -235878, 44152991]\) | \(82483294977/17\) | \(299136892617\) | \([2]\) | \(9216\) | \(1.5893\) | |
2601.g4 | 2601j4 | \([1, -1, 0, -1788, 1845125]\) | \(-35937/83521\) | \(-1469659553427321\) | \([2]\) | \(9216\) | \(1.5893\) |
Rank
sage: E.rank()
The elliptic curves in class 2601j have rank \(0\).
Complex multiplication
The elliptic curves in class 2601j do not have complex multiplication.Modular form 2601.2.a.j
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 Cremona 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 Cremona labels.