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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 301530.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.ba1 | 301530ba3 | \([1, 0, 1, -511819, 140864882]\) | \(100162392144121/23457780\) | \(3472593316266420\) | \([2]\) | \(6307840\) | \(1.9724\) | |
301530.ba2 | 301530ba4 | \([1, 0, 1, -236739, -43134014]\) | \(9912050027641/311647500\) | \(46135014717127500\) | \([2]\) | \(6307840\) | \(1.9724\) | |
301530.ba3 | 301530ba2 | \([1, 0, 1, -35719, 1653242]\) | \(34043726521/11696400\) | \(1731486972099600\) | \([2, 2]\) | \(3153920\) | \(1.6259\) | |
301530.ba4 | 301530ba1 | \([1, 0, 1, 6601, 180506]\) | \(214921799/218880\) | \(-32402095384320\) | \([2]\) | \(1576960\) | \(1.2793\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301530.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 301530.ba do not have complex multiplication.Modular form 301530.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.