Properties

Label 2070.h
Number of curves $4$
Conductor $2070$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2070.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.h1 2070i4 \([1, -1, 0, -12441699, 16894588693]\) \(292169767125103365085489/72534787200\) \(52877859868800\) \([2]\) \(57344\) \(2.4489\)  
2070.h2 2070i3 \([1, -1, 0, -910179, 168062485]\) \(114387056741228939569/49503729150000000\) \(36088218550350000000\) \([2]\) \(57344\) \(2.4489\)  
2070.h3 2070i2 \([1, -1, 0, -777699, 264057493]\) \(71356102305927901489/35540674560000\) \(25909151754240000\) \([2, 2]\) \(28672\) \(2.1024\)  
2070.h4 2070i1 \([1, -1, 0, -40419, 5567125]\) \(-10017490085065009/12502381363200\) \(-9114236013772800\) \([2]\) \(14336\) \(1.7558\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2070.h have rank \(0\).

Complex multiplication

The elliptic curves in class 2070.h do not have complex multiplication.

Modular form 2070.2.a.h

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.