Properties

Label 930.l
Number of curves $2$
Conductor $930$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 930.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.l1 930m2 \([1, 1, 1, -161, 119]\) \(461710681489/252204840\) \(252204840\) \([2]\) \(384\) \(0.30293\)  
930.l2 930m1 \([1, 1, 1, 39, 39]\) \(6549699311/4017600\) \(-4017600\) \([2]\) \(192\) \(-0.043649\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 930.l have rank \(1\).

Complex multiplication

The elliptic curves in class 930.l do not have complex multiplication.

Modular form 930.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - 6q^{11} - q^{12} - 2q^{13} + q^{15} + q^{16} - 4q^{17} + q^{18} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.