# Properties

 Label 30960bf Number of curves $4$ Conductor $30960$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bf1")

sage: E.isogeny_class()

## Elliptic curves in class 30960bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.f4 30960bf1 $$[0, 0, 0, -15483, 219818]$$ $$137467988281/72562500$$ $$216670464000000$$ $$[2]$$ $$92160$$ $$1.4423$$ $$\Gamma_0(N)$$-optimal
30960.f3 30960bf2 $$[0, 0, 0, -195483, 33231818]$$ $$276670733768281/336980250$$ $$1006217634816000$$ $$[2]$$ $$184320$$ $$1.7889$$
30960.f2 30960bf3 $$[0, 0, 0, -717483, -233913382]$$ $$13679527032530281/381633600$$ $$1139551823462400$$ $$[2]$$ $$276480$$ $$1.9917$$
30960.f1 30960bf4 $$[0, 0, 0, -746283, -214116262]$$ $$15393836938735081/2275690697640$$ $$6795176012101877760$$ $$[2]$$ $$552960$$ $$2.3382$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 30960.2.a.bf

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.