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Properties

Label 301530l
Number of curves $2$
Conductor $301530$
CM no
Rank $0$
Graph

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

Elliptic curves in class 301530l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301530.l2 301530l1 \([1, 1, 0, -52117, -5046419]\) \(-105756712489/12476160\) \(-1846919436906240\) \([2]\) \(2365440\) \(1.6652\) \(\Gamma_0(N)\)-optimal
301530.l1 301530l2 \([1, 1, 0, -856197, -305289891]\) \(468898230633769/5540400\) \(820178039415600\) \([2]\) \(4730880\) \(2.0117\)  

Rank

sage: E.rank()
 

The elliptic curves in class 301530l have rank \(0\).

Complex multiplication

The elliptic curves in class 301530l do not have complex multiplication.

Modular form 301530.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} - q^{10} + 6 q^{11} - q^{12} + 2 q^{14} - q^{15} + q^{16} - 2 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.