# Properties

 Label 466752cb Number of curves $2$ Conductor $466752$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 466752cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
466752.cb1 466752cb1 $$[0, -1, 0, -2525281, 1323593953]$$ $$6793805286030262681/1048227429629952$$ $$274786531312914137088$$ $$$$ $$28901376$$ $$2.6453$$ $$\Gamma_0(N)$$-optimal
466752.cb2 466752cb2 $$[0, -1, 0, 4396959, 7297487073]$$ $$35862531227445945959/108547797844556928$$ $$-28455153918163531333632$$ $$$$ $$57802752$$ $$2.9919$$

## Rank

sage: E.rank()

The elliptic curves in class 466752cb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 466752cb do not have complex multiplication.

## Modular form 466752.2.a.cb

sage: E.q_eigenform(10)

$$q - q^{3} + 4 q^{5} - 2 q^{7} + q^{9} - q^{11} + q^{13} - 4 q^{15} - q^{17} + 4 q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 