# Properties

 Label 47096c Number of curves $2$ Conductor $47096$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 47096c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.d1 47096c1 $$[0, 1, 0, -6167, -60770]$$ $$2725888/1421$$ $$13523903026256$$ $$$$ $$94080$$ $$1.2115$$ $$\Gamma_0(N)$$-optimal
47096.d2 47096c2 $$[0, 1, 0, 23268, -449312]$$ $$9148592/5887$$ $$-896441572026112$$ $$$$ $$188160$$ $$1.5581$$

## Rank

sage: E.rank()

The elliptic curves in class 47096c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 47096c do not have complex multiplication.

## Modular form 47096.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{3} + 2q^{5} - q^{7} + q^{9} + 6q^{13} - 4q^{15} - 4q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 