# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 12696.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.h1 12696a2 $$[0, -1, 0, -24676968, -47174799204]$$ $$10963069081334500/1156923$$ $$175376511804976128$$ $$$$ $$473088$$ $$2.7371$$
12696.h2 12696a1 $$[0, -1, 0, -1538508, -740537676]$$ $$-10627137250000/110008287$$ $$-4169004688233508608$$ $$$$ $$236544$$ $$2.3905$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 12696.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{7} + q^{9} + 2q^{13} - 8q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 