# Properties

 Label 960.h Number of curves $4$ Conductor $960$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 960.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.h1 960d3 $$[0, -1, 0, -1985, 19617]$$ $$26410345352/10546875$$ $$345600000000$$ $$$$ $$1536$$ $$0.91221$$
960.h2 960d2 $$[0, -1, 0, -905, -9975]$$ $$20034997696/455625$$ $$1866240000$$ $$[2, 2]$$ $$768$$ $$0.56564$$
960.h3 960d1 $$[0, -1, 0, -900, -10098]$$ $$1261112198464/675$$ $$43200$$ $$$$ $$384$$ $$0.21907$$ $$\Gamma_0(N)$$-optimal
960.h4 960d4 $$[0, -1, 0, 95, -31775]$$ $$2863288/13286025$$ $$-435356467200$$ $$$$ $$1536$$ $$0.91221$$

## Rank

sage: E.rank()

The elliptic curves in class 960.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 960.h do not have complex multiplication.

## Modular form960.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + 4 q^{7} + q^{9} + 4 q^{11} - 6 q^{13} - q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 