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Properties

Label 185130.h
Number of curves $2$
Conductor $185130$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 185130.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185130.h1 185130ec1 \([1, -1, 0, -717525, -185475339]\) \(42104603394468971/9020268000000\) \(8752357020132000000\) \([2]\) \(5308416\) \(2.3489\) \(\Gamma_0(N)\)-optimal
185130.h2 185130ec2 \([1, -1, 0, 1571355, -1128951675]\) \(442222574135797909/822972656250000\) \(-798529545386718750000\) \([2]\) \(10616832\) \(2.6955\)  

Rank

sage: E.rank()
 

The elliptic curves in class 185130.h have rank \(0\).

Complex multiplication

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

Modular form 185130.2.a.h

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.