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Properties

Label 95370bb
Number of curves $2$
Conductor $95370$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 95370bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95370.x2 95370bb1 \([1, 0, 1, 2161, -13174]\) \(13371532631/8660520\) \(-723335290920\) \([3]\) \(209952\) \(0.96449\) \(\Gamma_0(N)\)-optimal
95370.x1 95370bb2 \([1, 0, 1, -36854, -2806648]\) \(-66277326463129/2299968000\) \(-192095627328000\) \([]\) \(629856\) \(1.5138\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95370bb have rank \(1\).

Complex multiplication

The elliptic curves in class 95370bb do not have complex multiplication.

Modular form 95370.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + q^{12} - 4 q^{13} + 4 q^{14} - q^{15} + q^{16} - q^{18} - 4 q^{19} + O(q^{20})\) 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.