# Properties

 Label 960.m Number of curves $4$ Conductor $960$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 960.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.m1 960h3 $$[0, 1, 0, -1985, -19617]$$ $$26410345352/10546875$$ $$345600000000$$ $$$$ $$1536$$ $$0.91221$$
960.m2 960h2 $$[0, 1, 0, -905, 9975]$$ $$20034997696/455625$$ $$1866240000$$ $$[2, 2]$$ $$768$$ $$0.56564$$
960.m3 960h1 $$[0, 1, 0, -900, 10098]$$ $$1261112198464/675$$ $$43200$$ $$$$ $$384$$ $$0.21907$$ $$\Gamma_0(N)$$-optimal
960.m4 960h4 $$[0, 1, 0, 95, 31775]$$ $$2863288/13286025$$ $$-435356467200$$ $$$$ $$1536$$ $$0.91221$$

## Rank

sage: E.rank()

The elliptic curves in class 960.m have rank $$1$$.

## Complex multiplication

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

## Modular form960.2.a.m

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. 