Properties

Label 8470.h
Number of curves $2$
Conductor $8470$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.h1 8470b2 \([1, -1, 0, -820, 9246]\) \(45844273539/350\) \(465850\) \([2]\) \(3840\) \(0.26223\)  
8470.h2 8470b1 \([1, -1, 0, -50, 160]\) \(-10503459/980\) \(-1304380\) \([2]\) \(1920\) \(-0.084339\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8470.h have rank \(1\).

Complex multiplication

The elliptic curves in class 8470.h do not have complex multiplication.

Modular form 8470.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} - 3q^{9} + q^{10} - 6q^{13} + q^{14} + q^{16} + 6q^{17} + 3q^{18} + 6q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.