# Properties

 Label 2960.j Number of curves $3$ Conductor $2960$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("j1")

E.isogeny_class()

## Elliptic curves in class 2960.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2960.j1 2960j1 $$[0, -1, 0, -856, -9360]$$ $$-16954786009/370$$ $$-1515520$$ $$[]$$ $$864$$ $$0.30193$$ $$\Gamma_0(N)$$-optimal
2960.j2 2960j2 $$[0, -1, 0, -296, -21904]$$ $$-702595369/50653000$$ $$-207474688000$$ $$[]$$ $$2592$$ $$0.85124$$
2960.j3 2960j3 $$[0, -1, 0, 2664, 589040]$$ $$510273943271/37000000000$$ $$-151552000000000$$ $$[]$$ $$7776$$ $$1.4005$$

## Rank

sage: E.rank()

The elliptic curves in class 2960.j have rank $$1$$.

## Complex multiplication

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

## Modular form2960.2.a.j

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.