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Properties

Label 185130.ec
Number of curves $2$
Conductor $185130$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ec1")
 
E.isogeny_class()
 

Elliptic curves in class 185130.ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185130.ec1 185130bl2 \([1, -1, 1, -12806663, 17633175167]\) \(179865548102096641/119964240000\) \(154929973385428560000\) \([2]\) \(10321920\) \(2.8129\)  
185130.ec2 185130bl1 \([1, -1, 1, -958343, 159272831]\) \(75370704203521/35157196800\) \(45404393547029299200\) \([2]\) \(5160960\) \(2.4663\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 185130.ec have rank \(1\).

Complex multiplication

The elliptic curves in class 185130.ec do not have complex multiplication.

Modular form 185130.2.a.ec

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + 2 q^{7} + q^{8} - q^{10} + 4 q^{13} + 2 q^{14} + q^{16} + q^{17} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.