# Properties

 Label 6960.b Number of curves $2$ Conductor $6960$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("b1")

E.isogeny_class()

## Elliptic curves in class 6960.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6960.b1 6960v1 $$[0, -1, 0, -181, -899]$$ $$-160989184/3915$$ $$-16035840$$ $$[]$$ $$1440$$ $$0.16797$$ $$\Gamma_0(N)$$-optimal
6960.b2 6960v2 $$[0, -1, 0, 779, -4355]$$ $$12747309056/9145875$$ $$-37461504000$$ $$[]$$ $$4320$$ $$0.71728$$

## Rank

sage: E.rank()

The elliptic curves in class 6960.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6960.b do not have complex multiplication.

## Modular form6960.2.a.b

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.