# Properties

 Label 30960.r Number of curves $2$ Conductor $30960$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.r1 30960u2 $$[0, 0, 0, -3123, 46322]$$ $$30459021867/9245000$$ $$1022423040000$$ $$$$ $$36864$$ $$1.0095$$
30960.r2 30960u1 $$[0, 0, 0, -1203, -15502]$$ $$1740992427/68800$$ $$7608729600$$ $$$$ $$18432$$ $$0.66288$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 30960.r have rank $$1$$.

## Complex multiplication

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

## Modular form 30960.2.a.r

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{7} - 2q^{11} - 2q^{13} + 4q^{17} + O(q^{20})$$ ## 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. 