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Properties

Label 20070h
Number of curves $2$
Conductor $20070$
CM no
Rank $0$
Graph

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

Elliptic curves in class 20070h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20070.s1 20070h1 \([1, -1, 0, -1614, -23980]\) \(17227485284283/456704000\) \(12331008000\) \([2]\) \(24864\) \(0.71735\) \(\Gamma_0(N)\)-optimal
20070.s2 20070h2 \([1, -1, 0, 306, -78892]\) \(117145509957/99458000000\) \(-2685366000000\) \([2]\) \(49728\) \(1.0639\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20070h have rank \(0\).

Complex multiplication

The elliptic curves in class 20070h do not have complex multiplication.

Modular form 20070.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + 4 q^{7} - q^{8} - q^{10} - 4 q^{11} + 6 q^{13} - 4 q^{14} + q^{16} + 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.