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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 80937.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80937.q1 | 80937s4 | \([1, -1, 0, -431763, -109090504]\) | \(82483294977/17\) | \(1834608772377\) | \([2]\) | \(394240\) | \(1.7404\) | |
80937.q2 | 80937s2 | \([1, -1, 0, -27078, -1687105]\) | \(20346417/289\) | \(31188349130409\) | \([2, 2]\) | \(197120\) | \(1.3938\) | |
80937.q3 | 80937s3 | \([1, -1, 0, -3273, -4567510]\) | \(-35937/83521\) | \(-9013432898688201\) | \([2]\) | \(394240\) | \(1.7404\) | |
80937.q4 | 80937s1 | \([1, -1, 0, -3273, 31616]\) | \(35937/17\) | \(1834608772377\) | \([2]\) | \(98560\) | \(1.0473\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 80937.q have rank \(0\).
Complex multiplication
The elliptic curves in class 80937.q do not have complex multiplication.Modular form 80937.2.a.q
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.