# Properties

 Label 92400.gi Number of curves $2$ Conductor $92400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("gi1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.gi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.gi1 92400cx2 $$[0, 1, 0, -2099648, -1171729692]$$ $$7997484869919944276/116700507$$ $$14937664896000$$ $$$$ $$1142784$$ $$2.0797$$
92400.gi2 92400cx1 $$[0, 1, 0, -131348, -18305892]$$ $$7831544736466064/29831377653$$ $$954604084896000$$ $$$$ $$571392$$ $$1.7332$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92400.2.a.gi

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 