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Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 185130.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185130.s1 185130fo1 \([1, -1, 0, -145344315, -674406577179]\) \(-7099013253976488644787/133922877440\) \(-6405818760373063680\) \([]\) \(20736000\) \(3.1442\) \(\Gamma_0(N)\)-optimal
185130.s2 185130fo2 \([1, -1, 0, -136080555, -764104285675]\) \(-7992166558175554923/2608933282934000\) \(-90972551740516434208242000\) \([]\) \(62208000\) \(3.6935\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 185130.2.a.s

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.