# Properties

 Label 92400cm Number of curves $6$ Conductor $92400$ CM no Rank $0$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("cm1")

sage: E.isogeny_class()

## Elliptic curves in class 92400cm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.ic5 92400cm1 $$[0, 1, 0, 57617, -17512012]$$ $$84611246065664/580054565475$$ $$-145013641368750000$$ $$[2]$$ $$786432$$ $$1.9746$$ $$\Gamma_0(N)$$-optimal
92400.ic4 92400cm2 $$[0, 1, 0, -762508, -234025012]$$ $$12257375872392016/1191317675625$$ $$4765270702500000000$$ $$[2, 2]$$ $$1572864$$ $$2.3212$$
92400.ic3 92400cm3 $$[0, 1, 0, -2747008, 1492489988]$$ $$143279368983686884/22699269140625$$ $$363188306250000000000$$ $$[2, 2]$$ $$3145728$$ $$2.6678$$
92400.ic2 92400cm4 $$[0, 1, 0, -11900008, -15804250012]$$ $$11647843478225136004/128410942275$$ $$2054575076400000000$$ $$[2]$$ $$3145728$$ $$2.6678$$
92400.ic6 92400cm5 $$[0, 1, 0, 4875992, 8307451988]$$ $$400647648358480318/1163177490234375$$ $$-37221679687500000000000$$ $$[2]$$ $$6291456$$ $$3.0144$$
92400.ic1 92400cm6 $$[0, 1, 0, -42122008, 105206239988]$$ $$258286045443018193442/8440380939375$$ $$270092190060000000000$$ $$[2]$$ $$6291456$$ $$3.0144$$

## Rank

sage: E.rank()

The elliptic curves in class 92400cm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 92400cm do not have complex multiplication.

## Modular form 92400.2.a.cm

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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.