# Properties

 Label 1400.a Number of curves $2$ Conductor $1400$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 1400.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1400.a1 1400h2 $$[0, 1, 0, -1008, -12512]$$ $$3543122/49$$ $$1568000000$$ $$[2]$$ $$640$$ $$0.57005$$
1400.a2 1400h1 $$[0, 1, 0, -8, -512]$$ $$-4/7$$ $$-112000000$$ $$[2]$$ $$320$$ $$0.22348$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1400.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1400.a do not have complex multiplication.

## Modular form1400.2.a.a

sage: E.q_eigenform(10)

$$q - 2 q^{3} - q^{7} + q^{9} + 2 q^{17} - 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.