# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.o1 30960bl1 $$[0, 0, 0, -22251963, -40299850262]$$ $$408076159454905367161/1190206406250000$$ $$3553937285760000000000$$ $$$$ $$2027520$$ $$3.0057$$ $$\Gamma_0(N)$$-optimal
30960.o2 30960bl2 $$[0, 0, 0, -13251963, -73198450262]$$ $$-86193969101536367161/725294740213012500$$ $$-2165718489560211916800000$$ $$$$ $$4055040$$ $$3.3523$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 30960.2.a.o

sage: E.q_eigenform(10)

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