# Properties

 Label 92575.m Number of curves $3$ Conductor $92575$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 92575.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92575.m1 92575n3 $$[0, -1, 1, -1736883, 922243293]$$ $$-250523582464/13671875$$ $$-31623877655029296875$$ $$[]$$ $$1710720$$ $$2.4999$$
92575.m2 92575n1 $$[0, -1, 1, -17633, -993957]$$ $$-262144/35$$ $$-80957126796875$$ $$[]$$ $$190080$$ $$1.4013$$ $$\Gamma_0(N)$$-optimal
92575.m3 92575n2 $$[0, -1, 1, 114617, 2510668]$$ $$71991296/42875$$ $$-99172480326171875$$ $$[]$$ $$570240$$ $$1.9506$$

## Rank

sage: E.rank()

The elliptic curves in class 92575.m have rank $$1$$.

## Complex multiplication

The elliptic curves in class 92575.m do not have complex multiplication.

## Modular form 92575.2.a.m

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{4} + q^{7} - 2q^{9} + 3q^{11} + 2q^{12} - 5q^{13} + 4q^{16} + 3q^{17} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 