# Properties

 Label 1470h Number of curves $4$ Conductor $1470$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1470h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1470.g3 1470h1 [1, 0, 1, -173, 536] [2] 768 $$\Gamma_0(N)$$-optimal
1470.g2 1470h2 [1, 0, 1, -1153, -14752] [2, 2] 1536
1470.g1 1470h3 [1, 0, 1, -18303, -954572] [2] 3072
1470.g4 1470h4 [1, 0, 1, 317, -49444] [2] 3072

## Rank

sage: E.rank()

The elliptic curves in class 1470h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1470h do not have complex multiplication.

## Modular form1470.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} + 2q^{13} + q^{15} + q^{16} + 6q^{17} - q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.