# Properties

 Label 12696.t Number of curves $4$ Conductor $12696$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 12696.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.t1 12696q3 $$[0, 1, 0, -1557552, -748709472]$$ $$1378334691074/69$$ $$20919247546368$$ $$$$ $$135168$$ $$2.0304$$
12696.t2 12696q4 $$[0, 1, 0, -160992, 5331360]$$ $$1522096994/839523$$ $$254524484896659456$$ $$$$ $$135168$$ $$2.0304$$
12696.t3 12696q2 $$[0, 1, 0, -97512, -11681280]$$ $$676449508/4761$$ $$721714040349696$$ $$[2, 2]$$ $$67584$$ $$1.6838$$
12696.t4 12696q1 $$[0, 1, 0, -2292, -407232]$$ $$-35152/1863$$ $$-70602460468992$$ $$$$ $$33792$$ $$1.3373$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 12696.2.a.t

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 