# Properties

 Label 30960.bl Number of curves $2$ Conductor $30960$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.bl1 30960x2 $$[0, 0, 0, -46467, 3854466]$$ $$137627865747/36980$$ $$2981385584640$$ $$[2]$$ $$73728$$ $$1.3771$$
30960.bl2 30960x1 $$[0, 0, 0, -3267, 44226]$$ $$47832147/17200$$ $$1386690969600$$ $$[2]$$ $$36864$$ $$1.0306$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 30960.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{5} - 6q^{13} + 2q^{17} - 2q^{19} + O(q^{20})$$

## 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.