# Properties

 Label 46800cb Number of curves $4$ Conductor $46800$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 46800cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.m4 46800cb1 $$[0, 0, 0, 38925, 2307250]$$ $$3774555693/3515200$$ $$-6074265600000000$$ $$[2]$$ $$331776$$ $$1.7158$$ $$\Gamma_0(N)$$-optimal
46800.m3 46800cb2 $$[0, 0, 0, -201075, 20787250]$$ $$520300455507/193072360$$ $$333629038080000000$$ $$[2]$$ $$663552$$ $$2.0624$$
46800.m2 46800cb3 $$[0, 0, 0, -897075, 330635250]$$ $$-63378025803/812500$$ $$-1023516000000000000$$ $$[2]$$ $$995328$$ $$2.2651$$
46800.m1 46800cb4 $$[0, 0, 0, -14397075, 21026135250]$$ $$261984288445803/42250$$ $$53222832000000000$$ $$[2]$$ $$1990656$$ $$2.6117$$

## Rank

sage: E.rank()

The elliptic curves in class 46800cb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 46800cb do not have complex multiplication.

## Modular form 46800.2.a.cb

sage: E.q_eigenform(10)

$$q - 4q^{7} - q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.