# Properties

 Label 247962a Number of curves $2$ Conductor $247962$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 247962a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.a1 247962a1 $$[1, 1, 0, -27027, -1229475]$$ $$90458382169/25788048$$ $$622460787975312$$ $$$$ $$1843200$$ $$1.5454$$ $$\Gamma_0(N)$$-optimal
247962.a2 247962a2 $$[1, 1, 0, 71233, -8009415]$$ $$1656015369191/2114999172$$ $$-51050938449092868$$ $$$$ $$3686400$$ $$1.8919$$

## Rank

sage: E.rank()

The elliptic curves in class 247962a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 247962a do not have complex multiplication.

## Modular form 247962.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - 4q^{5} + q^{6} - q^{8} + q^{9} + 4q^{10} - q^{11} - q^{12} - q^{13} + 4q^{15} + q^{16} - q^{18} + 2q^{19} + O(q^{20})$$ ## 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 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. 