# Properties

 Label 369600.mh Number of curves $4$ Conductor $369600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("mh1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.mh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.mh1 369600mh3 $$[0, 1, 0, -14901633, -21906511137]$$ $$89343998142858649/1112702976000$$ $$4557631389696000000000$$ $$$$ $$23887872$$ $$2.9657$$
369600.mh2 369600mh4 $$[0, 1, 0, -2613633, -56939599137]$$ $$-482056280171929/341652696000000$$ $$-1399409442816000000000000$$ $$$$ $$47775744$$ $$3.3122$$
369600.mh3 369600mh1 $$[0, 1, 0, -1437633, 647272863]$$ $$80224711835689/2173469760$$ $$8902532136960000000$$ $$$$ $$7962624$$ $$2.4164$$ $$\Gamma_0(N)$$-optimal
369600.mh4 369600mh2 $$[0, 1, 0, 290367, 2107432863]$$ $$661003929431/468755040600$$ $$-1920020646297600000000$$ $$$$ $$15925248$$ $$2.7629$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 369600.2.a.mh

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 