# Properties

 Label 32340.c Number of curves $2$ Conductor $32340$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 32340.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.c1 32340d2 $$[0, -1, 0, -11076, 452376]$$ $$1711503051568/7425$$ $$651974400$$ $$$$ $$32256$$ $$0.89810$$
32340.c2 32340d1 $$[0, -1, 0, -681, 7470]$$ $$-6373654528/441045$$ $$-2420454960$$ $$$$ $$16128$$ $$0.55152$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32340.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 32340.c do not have complex multiplication.

## Modular form 32340.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - q^{11} + 6q^{13} + q^{15} + 2q^{17} - 2q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 