# Properties

 Label 92400cr Number of curves $2$ Conductor $92400$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cr1")

sage: E.isogeny_class()

## Elliptic curves in class 92400cr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.en1 92400cr1 $$[0, 1, 0, -111083, -14286912]$$ $$4850878539776/130977$$ $$4093031250000$$ $$$$ $$332800$$ $$1.5243$$ $$\Gamma_0(N)$$-optimal
92400.en2 92400cr2 $$[0, 1, 0, -106708, -15459412]$$ $$-268750151696/50014503$$ $$-25007251500000000$$ $$$$ $$665600$$ $$1.8709$$

## Rank

sage: E.rank()

The elliptic curves in class 92400cr have rank $$1$$.

## Complex multiplication

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

## Modular form 92400.2.a.cr

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 