# Properties

 Label 12696.n Number of curves $2$ Conductor $12696$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 12696.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.n1 12696l1 $$[0, -1, 0, -105447, -13075920]$$ $$4499456/27$$ $$778097949752016$$ $$$$ $$52992$$ $$1.6967$$ $$\Gamma_0(N)$$-optimal
12696.n2 12696l2 $$[0, -1, 0, -44612, -28114332]$$ $$-21296/729$$ $$-336138314292870912$$ $$$$ $$105984$$ $$2.0433$$

## Rank

sage: E.rank()

The elliptic curves in class 12696.n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 12696.n do not have complex multiplication.

## Modular form 12696.2.a.n

sage: E.q_eigenform(10)

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