# Properties

 Label 88935.cb Number of curves $2$ Conductor $88935$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 88935.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.cb1 88935s2 $$[0, -1, 1, -158839886, -14567227396723]$$ $$-2126464142970105856/438611057788643355$$ $$-91416360597662969163474158595$$ $$[]$$ $$172800000$$ $$4.2364$$
88935.cb2 88935s1 $$[0, -1, 1, -53007236, 173973325217]$$ $$-79028701534867456/16987307596875$$ $$-3540535080644638438621875$$ $$[]$$ $$34560000$$ $$3.4317$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 88935.cb have rank $$1$$.

## Complex multiplication

The elliptic curves in class 88935.cb do not have complex multiplication.

## Modular form 88935.2.a.cb

sage: E.q_eigenform(10)

$$q + 2q^{2} - q^{3} + 2q^{4} - q^{5} - 2q^{6} + q^{9} - 2q^{10} - 2q^{12} - 6q^{13} + q^{15} - 4q^{16} - 7q^{17} + 2q^{18} - 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.