Properties

 Label 2400.c Number of curves $2$ Conductor $2400$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 2400.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.c1 2400y2 $$[0, -1, 0, -48, -108]$$ $$195112/9$$ $$576000$$ $$$$ $$384$$ $$-0.13318$$
2400.c2 2400y1 $$[0, -1, 0, 2, -8]$$ $$64/3$$ $$-24000$$ $$$$ $$192$$ $$-0.47976$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2400.c have rank $$1$$.

Complex multiplication

The elliptic curves in class 2400.c do not have complex multiplication.

Modular form2400.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} - 2 q^{7} + q^{9} - 6 q^{11} + 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})$$ 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. 