# Properties

 Label 6930h Number of curves $4$ Conductor $6930$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6930h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.f4 6930h1 $$[1, -1, 0, 90, -2700]$$ $$109902239/4312000$$ $$-3143448000$$ $$[2]$$ $$4608$$ $$0.50224$$ $$\Gamma_0(N)$$-optimal
6930.f2 6930h2 $$[1, -1, 0, -2430, -43524]$$ $$2177286259681/105875000$$ $$77182875000$$ $$[2]$$ $$9216$$ $$0.84882$$
6930.f3 6930h3 $$[1, -1, 0, -810, 73440]$$ $$-80677568161/3131816380$$ $$-2283094141020$$ $$[6]$$ $$13824$$ $$1.0515$$
6930.f1 6930h4 $$[1, -1, 0, -31680, 2166426]$$ $$4823468134087681/30382271150$$ $$22148675668350$$ $$[6]$$ $$27648$$ $$1.3981$$

## Rank

sage: E.rank()

The elliptic curves in class 6930h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6930h do not have complex multiplication.

## Modular form6930.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} + q^{11} + 2 q^{13} - q^{14} + q^{16} - 6 q^{17} + 2 q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.