# Properties

 Label 78400.gm Number of curves $4$ Conductor $78400$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gm1")

sage: E.isogeny_class()

## Elliptic curves in class 78400.gm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
78400.gm1 78400u4 [0, 0, 0, -1465100, -682570000]  786432
78400.gm2 78400u3 [0, 0, 0, -289100, 47334000]  786432
78400.gm3 78400u2 [0, 0, 0, -93100, -10290000] [2, 2] 393216
78400.gm4 78400u1 [0, 0, 0, 4900, -686000]  196608 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 78400.gm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 78400.gm do not have complex multiplication.

## Modular form 78400.2.a.gm

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 