# Properties

 Label 6400.l Number of curves $2$ Conductor $6400$ CM $$\Q(\sqrt{-1})$$ Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 6400.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
6400.l1 6400m2 $$[0, 0, 0, -200, 0]$$ $$1728$$ $$512000000$$ $$$$ $$1280$$ $$0.36062$$   $$-4$$
6400.l2 6400m1 $$[0, 0, 0, 50, 0]$$ $$1728$$ $$-8000000$$ $$$$ $$640$$ $$0.014046$$ $$\Gamma_0(N)$$-optimal $$-4$$

## Rank

sage: E.rank()

The elliptic curves in class 6400.l have rank $$0$$.

## Complex multiplication

Each elliptic curve in class 6400.l has complex multiplication by an order in the imaginary quadratic field $$\Q(\sqrt{-1})$$.

## Modular form6400.2.a.l

sage: E.q_eigenform(10)

$$q - 3q^{9} - 4q^{13} + 2q^{17} + O(q^{20})$$ ## 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. 