# Properties

 Label 90480.cb Number of curves $4$ Conductor $90480$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cb1")

sage: E.isogeny_class()

## Elliptic curves in class 90480.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90480.cb1 90480cc4 $$[0, 1, 0, -133640, 17171700]$$ $$64443098670429961/6032611833300$$ $$24709578069196800$$ $$[4]$$ $$1179648$$ $$1.8839$$
90480.cb2 90480cc2 $$[0, 1, 0, -29640, -1673100]$$ $$703093388853961/115124490000$$ $$471549911040000$$ $$[2, 2]$$ $$589824$$ $$1.5373$$
90480.cb3 90480cc1 $$[0, 1, 0, -28360, -1847692]$$ $$615882348586441/21715200$$ $$88945459200$$ $$[2]$$ $$294912$$ $$1.1907$$ $$\Gamma_0(N)$$-optimal
90480.cb4 90480cc3 $$[0, 1, 0, 53880, -9323532]$$ $$4223169036960119/11647532812500$$ $$-47708294400000000$$ $$[2]$$ $$1179648$$ $$1.8839$$

## Rank

sage: E.rank()

The elliptic curves in class 90480.cb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 90480.cb do not have complex multiplication.

## Modular form 90480.2.a.cb

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + 4 q^{7} + q^{9} + 4 q^{11} + q^{13} + q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.