# Properties

 Label 2960.g Number of curves $4$ Conductor $2960$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 2960.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2960.g1 2960e3 $$[0, 0, 0, -6323, 193522]$$ $$6825481747209/46250$$ $$189440000$$ $$$$ $$1536$$ $$0.76966$$
2960.g2 2960e2 $$[0, 0, 0, -403, 2898]$$ $$1767172329/136900$$ $$560742400$$ $$[2, 2]$$ $$768$$ $$0.42308$$
2960.g3 2960e1 $$[0, 0, 0, -83, -238]$$ $$15438249/2960$$ $$12124160$$ $$$$ $$384$$ $$0.076511$$ $$\Gamma_0(N)$$-optimal
2960.g4 2960e4 $$[0, 0, 0, 397, 12978]$$ $$1689410871/18741610$$ $$-76765634560$$ $$$$ $$1536$$ $$0.76966$$

## Rank

sage: E.rank()

The elliptic curves in class 2960.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2960.g do not have complex multiplication.

## Modular form2960.2.a.g

sage: E.q_eigenform(10)

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