# Properties

 Label 92400.z Number of curves 4 Conductor 92400 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("92400.z1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92400.z1 92400dw4 [0, -1, 0, -13196408, -18446876688] [2] 3538944
92400.z2 92400dw2 [0, -1, 0, -848408, -270620688] [2, 2] 1769472
92400.z3 92400dw1 [0, -1, 0, -200408, 30051312] [2] 884736 $$\Gamma_0(N)$$-optimal
92400.z4 92400dw3 [0, -1, 0, 1131592, -1347740688] [2] 3538944

## Rank

sage: E.rank()

The elliptic curves in class 92400.z have rank $$1$$.

## Modular form 92400.2.a.z

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.