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Properties

Label 95550.s
Number of curves $2$
Conductor $95550$
CM no
Rank $1$
Graph

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

Elliptic curves in class 95550.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.s1 95550c1 \([1, 1, 0, -1332825, 596377125]\) \(-11167382937025/102503232\) \(-2403420508125000000\) \([]\) \(2643840\) \(2.3494\) \(\Gamma_0(N)\)-optimal
95550.s2 95550c2 \([1, 1, 0, 4179675, 3148664625]\) \(344396625134975/381761977428\) \(-8951274490279570312500\) \([]\) \(7931520\) \(2.8987\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95550.s have rank \(1\).

Complex multiplication

The elliptic curves in class 95550.s do not have complex multiplication.

Modular form 95550.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 3 q^{11} - q^{12} - q^{13} + q^{16} + 3 q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) 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.