# Properties

 Label 400.c Number of curves $4$ Conductor $400$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 400.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
400.c1 400e3 $$[0, 1, 0, -1033, 12438]$$ $$488095744/125$$ $$31250000$$ $$$$ $$144$$ $$0.42408$$
400.c2 400e4 $$[0, 1, 0, -908, 15688]$$ $$-20720464/15625$$ $$-62500000000$$ $$$$ $$288$$ $$0.77065$$
400.c3 400e1 $$[0, 1, 0, -33, -62]$$ $$16384/5$$ $$1250000$$ $$$$ $$48$$ $$-0.12523$$ $$\Gamma_0(N)$$-optimal
400.c4 400e2 $$[0, 1, 0, 92, -312]$$ $$21296/25$$ $$-100000000$$ $$$$ $$96$$ $$0.22134$$

## Rank

sage: E.rank()

The elliptic curves in class 400.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 400.c do not have complex multiplication.

## Modular form400.2.a.c

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 