# Properties

 Label 12696.a Number of curves $2$ Conductor $12696$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 12696.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.a1 12696i2 $$[0, -1, 0, -29800, 1843996]$$ $$19307236/1587$$ $$240571346783232$$ $$$$ $$67584$$ $$1.5020$$
12696.a2 12696i1 $$[0, -1, 0, 1940, 130036]$$ $$21296/207$$ $$-7844717829888$$ $$$$ $$33792$$ $$1.1554$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 12696.a have rank $$0$$.

## Complex multiplication

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

## Modular form 12696.2.a.a

sage: E.q_eigenform(10)

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