# Properties

 Label 30960.a Number of curves $2$ Conductor $30960$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.a1 30960br1 $$[0, 0, 0, -3243, 69658]$$ $$1263214441/29025$$ $$86668185600$$ $$[2]$$ $$36864$$ $$0.88511$$ $$\Gamma_0(N)$$-optimal
30960.a2 30960br2 $$[0, 0, 0, 357, 215818]$$ $$1685159/6739605$$ $$-20124352696320$$ $$[2]$$ $$73728$$ $$1.2317$$

## Rank

sage: E.rank()

The elliptic curves in class 30960.a have rank $$2$$.

## Complex multiplication

The elliptic curves in class 30960.a do not have complex multiplication.

## Modular form 30960.2.a.a

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} - 2q^{11} + 2q^{13} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.