# Properties

 Label 1216.n Number of curves $2$ Conductor $1216$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("n1")

E.isogeny_class()

## Elliptic curves in class 1216.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1216.n1 1216f2 $$[0, 1, 0, -4481, -129313]$$ $$-37966934881/4952198$$ $$-1298188992512$$ $$[]$$ $$1920$$ $$1.0575$$
1216.n2 1216f1 $$[0, 1, 0, -1, 607]$$ $$-1/608$$ $$-159383552$$ $$[]$$ $$384$$ $$0.25279$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1216.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1216.n do not have complex multiplication.

## Modular form1216.2.a.n

sage: E.q_eigenform(10)

$$q + q^{3} + 4 q^{5} + 3 q^{7} - 2 q^{9} - 2 q^{11} + q^{13} + 4 q^{15} + 3 q^{17} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 