Properties

Label 301530.ba
Number of curves $4$
Conductor $301530$
CM no
Rank $0$
Graph

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Show commands: 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)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 4 q^{7} - q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} - 6 q^{13} - 4 q^{14} - q^{15} + q^{16} + 6 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display

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.