# Properties

 Label 1568.h Number of curves $2$ Conductor $1568$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1568.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1568.h1 1568c2 $$[0, -1, 0, -408, 1940]$$ $$125000/49$$ $$2951578112$$ $$$$ $$768$$ $$0.51575$$
1568.h2 1568c1 $$[0, -1, 0, 82, 176]$$ $$8000/7$$ $$-52706752$$ $$$$ $$384$$ $$0.16918$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1568.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1568.h do not have complex multiplication.

## Modular form1568.2.a.h

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{9} - 4q^{11} + 4q^{13} + 2q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 