# Properties

 Label 327990bc Number of curves $2$ Conductor $327990$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 327990bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bc1 327990bc1 $$[1, 1, 1, -700150, 191543027]$$ $$63812982460681/10201800960$$ $$6068269127208188160$$ $$$$ $$6451200$$ $$2.3265$$ $$\Gamma_0(N)$$-optimal
327990.bc2 327990bc2 $$[1, 1, 1, 1250970, 1070327475]$$ $$363979050334199/1041836936400$$ $$-619708906449913784400$$ $$$$ $$12902400$$ $$2.6731$$

## Rank

sage: E.rank()

The elliptic curves in class 327990bc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 327990bc do not have complex multiplication.

## Modular form 327990.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 4 q^{11} - q^{12} - q^{13} - q^{15} + q^{16} + 4 q^{17} + q^{18} + O(q^{20})$$ ## 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. 