# Properties

 Label 75348.g Number of curves $2$ Conductor $75348$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 75348.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75348.g1 75348c2 $$[0, 0, 0, -3015, -5346]$$ $$16241202000/9332687$$ $$1741703378688$$ $$$$ $$92160$$ $$1.0385$$
75348.g2 75348c1 $$[0, 0, 0, -1980, 33777]$$ $$73598976000/336973$$ $$3930453072$$ $$$$ $$46080$$ $$0.69188$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 75348.g have rank $$2$$.

## Complex multiplication

The elliptic curves in class 75348.g do not have complex multiplication.

## Modular form 75348.2.a.g

sage: E.q_eigenform(10)

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