# Properties

 Label 1078.h Number of curves $2$ Conductor $1078$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 1078.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1078.h1 1078m2 $$[1, 0, 0, -2794, -22506]$$ $$59776471/29282$$ $$1181634320174$$ $$[2]$$ $$1792$$ $$1.0098$$
1078.h2 1078m1 $$[1, 0, 0, 636, -2612]$$ $$704969/484$$ $$-19531145788$$ $$[2]$$ $$896$$ $$0.66322$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1078.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1078.h do not have complex multiplication.

## Modular form1078.2.a.h

sage: E.q_eigenform(10)

$$q + q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - 2 q^{6} + q^{8} + q^{9} - 2 q^{10} + q^{11} - 2 q^{12} + 2 q^{13} + 4 q^{15} + q^{16} + q^{18} - 2 q^{19} + O(q^{20})$$

## 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.