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Properties

Label 95370.h
Number of curves $2$
Conductor $95370$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 95370.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95370.h1 95370g1 \([1, 1, 0, -29628, 1986228]\) \(-119168121961/2524500\) \(-60935292940500\) \([]\) \(414720\) \(1.4355\) \(\Gamma_0(N)\)-optimal
95370.h2 95370g2 \([1, 1, 0, 122097, 9056613]\) \(8339492177639/6277634880\) \(-151526845072806720\) \([]\) \(1244160\) \(1.9848\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95370.h have rank \(2\).

Complex multiplication

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

Modular form 95370.2.a.h

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