# Properties

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

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 $$[1, -1, 0, -12441699, 16894588693]$$ $$292169767125103365085489/72534787200$$ $$52877859868800$$ $$$$ $$57344$$ $$2.4489$$
2070.h2 2070i3 $$[1, -1, 0, -910179, 168062485]$$ $$114387056741228939569/49503729150000000$$ $$36088218550350000000$$ $$$$ $$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$$ $$$$ $$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 form2070.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 6q^{13} + q^{16} - 2q^{17} + O(q^{20})$$ ## 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. 