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Properties

Label 5070h
Number of curves $2$
Conductor $5070$
CM no
Rank $1$
Graph

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

Elliptic curves in class 5070h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.h1 5070h1 \([1, 1, 0, -3795912, -2743222464]\) \(570403428460237/23887872000\) \(253318923646304256000\) \([2]\) \(336960\) \(2.6799\) \(\Gamma_0(N)\)-optimal
5070.h2 5070h2 \([1, 1, 0, 1828408, -10170699456]\) \(63745936931123/4251528000000\) \(-45085326010291944000000\) \([2]\) \(673920\) \(3.0265\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5070h have rank \(1\).

Complex multiplication

The elliptic curves in class 5070h do not have complex multiplication.

Modular form 5070.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} + 6 q^{11} - q^{12} - q^{15} + q^{16} + 6 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.