# Properties

 Label 369600.tc Number of curves $4$ Conductor $369600$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("tc1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.tc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.tc1 369600tc3 $$[0, 1, 0, -1629469633, 22422540588863]$$ $$233632133015204766393938/29145526885986328125$$ $$59690039062500000000000000000$$ $$[2]$$ $$377487360$$ $$4.2512$$
369600.tc2 369600tc2 $$[0, 1, 0, -407017633, -2797866623137]$$ $$7282213870869695463556/912102595400390625$$ $$933993057690000000000000000$$ $$[2, 2]$$ $$188743680$$ $$3.9047$$
369600.tc3 369600tc1 $$[0, 1, 0, -393895633, -3009065213137]$$ $$26401417552259125806544/507547744790625$$ $$129932222666400000000000$$ $$[2]$$ $$94371840$$ $$3.5581$$ $$\Gamma_0(N)$$-optimal
369600.tc4 369600tc4 $$[0, 1, 0, 605482367, -14501354123137]$$ $$11986661998777424518222/51295853620928503125$$ $$-105053908215661574400000000000$$ $$[2]$$ $$377487360$$ $$4.2512$$

## Rank

sage: E.rank()

The elliptic curves in class 369600.tc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 369600.tc do not have complex multiplication.

## Modular form 369600.2.a.tc

sage: E.q_eigenform(10)

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

## 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.