Properties

 Label 2072.c Number of curves $2$ Conductor $2072$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

Elliptic curves in class 2072.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2072.c1 2072a1 $$[0, 0, 0, -10, 9]$$ $$6912000/1813$$ $$29008$$ $$$$ $$112$$ $$-0.43491$$ $$\Gamma_0(N)$$-optimal
2072.c2 2072a2 $$[0, 0, 0, 25, 58]$$ $$6750000/9583$$ $$-2453248$$ $$$$ $$224$$ $$-0.088339$$

Rank

sage: E.rank()

The elliptic curves in class 2072.c have rank $$1$$.

Complex multiplication

The elliptic curves in class 2072.c do not have complex multiplication.

Modular form2072.2.a.c

sage: E.q_eigenform(10)

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