# Properties

 Label 12696.i Number of curves $2$ Conductor $12696$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 12696.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.i1 12696d2 $$[0, -1, 0, -605352, 181458540]$$ $$80919167474/14283$$ $$4330284242098176$$ $$[2]$$ $$101376$$ $$2.0052$$
12696.i2 12696d1 $$[0, -1, 0, -34032, 3435228]$$ $$-28756228/16767$$ $$-2541688576883712$$ $$[2]$$ $$50688$$ $$1.6586$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 12696.2.a.i

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - 2q^{7} + q^{9} + 2q^{11} - 2q^{13} - 2q^{15} + 4q^{17} + O(q^{20})$$

## 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.