# Properties

 Label 3120.q Number of curves $4$ Conductor $3120$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("q1")

E.isogeny_class()

## Elliptic curves in class 3120.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.q1 3120u3 $$[0, 1, 0, -7736, 259284]$$ $$12501706118329/2570490$$ $$10528727040$$ $$$$ $$3072$$ $$0.92018$$
3120.q2 3120u2 $$[0, 1, 0, -536, 2964]$$ $$4165509529/1368900$$ $$5607014400$$ $$[2, 2]$$ $$1536$$ $$0.57361$$
3120.q3 3120u1 $$[0, 1, 0, -216, -1260]$$ $$273359449/9360$$ $$38338560$$ $$$$ $$768$$ $$0.22703$$ $$\Gamma_0(N)$$-optimal
3120.q4 3120u4 $$[0, 1, 0, 1544, 22100]$$ $$99317171591/106616250$$ $$-436700160000$$ $$$$ $$3072$$ $$0.92018$$

## Rank

sage: E.rank()

The elliptic curves in class 3120.q have rank $$1$$.

## Complex multiplication

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

## Modular form3120.2.a.q

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - q^{13} - q^{15} - 6 q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 