# Properties

 Label 1400a Number of curves $4$ Conductor $1400$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1400a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1400.g4 1400a1 [0, 0, 0, 25, 250]  256 $$\Gamma_0(N)$$-optimal
1400.g3 1400a2 [0, 0, 0, -475, 3750] [2, 2] 512
1400.g2 1400a3 [0, 0, 0, -1475, -17250]  1024
1400.g1 1400a4 [0, 0, 0, -7475, 248750]  1024

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1400.2.a.a

sage: E.q_eigenform(10)

$$q + q^{7} - 3q^{9} - 4q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 