# Properties

 Label 840.c Number of curves $4$ Conductor $840$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 840.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
840.c1 840b3 $$[0, -1, 0, -3736, -86660]$$ $$5633270409316/14175$$ $$14515200$$ $$$$ $$512$$ $$0.61247$$
840.c2 840b4 $$[0, -1, 0, -656, 4956]$$ $$30534944836/8203125$$ $$8400000000$$ $$$$ $$512$$ $$0.61247$$
840.c3 840b2 $$[0, -1, 0, -236, -1260]$$ $$5702413264/275625$$ $$70560000$$ $$[2, 2]$$ $$256$$ $$0.26590$$
840.c4 840b1 $$[0, -1, 0, 9, -84]$$ $$4499456/180075$$ $$-2881200$$ $$$$ $$128$$ $$-0.080674$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 840.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 840.c do not have complex multiplication.

## Modular form840.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} - 2q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 