Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2400.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2400.i1 | 2400a3 | \([0, -1, 0, -4008, 99012]\) | \(890277128/15\) | \(120000000\) | \([4]\) | \(1536\) | \(0.68052\) | |
2400.i2 | 2400a2 | \([0, -1, 0, -1008, -10488]\) | \(14172488/1875\) | \(15000000000\) | \([2]\) | \(1536\) | \(0.68052\) | |
2400.i3 | 2400a1 | \([0, -1, 0, -258, 1512]\) | \(1906624/225\) | \(225000000\) | \([2, 2]\) | \(768\) | \(0.33395\) | \(\Gamma_0(N)\)-optimal |
2400.i4 | 2400a4 | \([0, -1, 0, 367, 7137]\) | \(85184/405\) | \(-25920000000\) | \([2]\) | \(1536\) | \(0.68052\) |
Rank
sage: E.rank()
The elliptic curves in class 2400.i have rank \(1\).
Complex multiplication
The elliptic curves in class 2400.i do not have complex multiplication.Modular form 2400.2.a.i
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.