# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 12696t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.q2 12696t1 $$[0, 1, 0, 4056, -6196608]$$ $$4/9$$ $$-16599422928043008$$ $$$$ $$105984$$ $$1.7913$$ $$\Gamma_0(N)$$-optimal
12696.q1 12696t2 $$[0, 1, 0, -482624, -126503904]$$ $$3370318/81$$ $$298789612704774144$$ $$$$ $$211968$$ $$2.1379$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 12696.2.a.t

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + 4q^{7} + q^{9} + 2q^{11} + 6q^{13} - 2q^{15} - 6q^{19} + O(q^{20})$$ ## 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 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. 