# Properties

 Label 30960.i Number of curves $2$ Conductor $30960$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.i1 30960a2 $$[0, 0, 0, -663, -6538]$$ $$4662947952/26875$$ $$185760000$$ $$$$ $$8192$$ $$0.42778$$
30960.i2 30960a1 $$[0, 0, 0, -18, -217]$$ $$-1492992/46225$$ $$-19969200$$ $$$$ $$4096$$ $$0.081202$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 30960.i have rank $$0$$.

## Complex multiplication

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

## Modular form 30960.2.a.i

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 