# Properties

 Label 3120.s Number of curves $4$ Conductor $3120$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 3120.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.s1 3120k3 $$[0, 1, 0, -8320, -294892]$$ $$31103978031362/195$$ $$399360$$ $$$$ $$3072$$ $$0.68038$$
3120.s2 3120k4 $$[0, 1, 0, -720, -972]$$ $$20183398562/11567205$$ $$23689635840$$ $$$$ $$3072$$ $$0.68038$$
3120.s3 3120k2 $$[0, 1, 0, -520, -4732]$$ $$15214885924/38025$$ $$38937600$$ $$[2, 2]$$ $$1536$$ $$0.33381$$
3120.s4 3120k1 $$[0, 1, 0, -20, -132]$$ $$-3631696/24375$$ $$-6240000$$ $$$$ $$768$$ $$-0.012768$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3120.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3120.s do not have complex multiplication.

## Modular form3120.2.a.s

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 