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Properties

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

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 95550cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.bs2 95550cg1 \([1, 1, 0, 14675, 14747125]\) \(7604375/2047032\) \(-94074713971875000\) \([]\) \(933120\) \(1.9361\) \(\Gamma_0(N)\)-optimal
95550.bs1 95550cg2 \([1, 1, 0, -4119700, 3217234000]\) \(-168256703745625/30371328\) \(-1395764206200000000\) \([]\) \(2799360\) \(2.4854\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 95550.2.a.cg

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