Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 480.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480.d1 | 480b2 | \([0, -1, 0, -160, -728]\) | \(890277128/15\) | \(7680\) | \([2]\) | \(64\) | \(-0.12420\) | |
480.d2 | 480b3 | \([0, -1, 0, -40, 100]\) | \(14172488/1875\) | \(960000\) | \([4]\) | \(64\) | \(-0.12420\) | |
480.d3 | 480b1 | \([0, -1, 0, -10, -8]\) | \(1906624/225\) | \(14400\) | \([2, 2]\) | \(32\) | \(-0.47077\) | \(\Gamma_0(N)\)-optimal |
480.d4 | 480b4 | \([0, -1, 0, 15, -63]\) | \(85184/405\) | \(-1658880\) | \([2]\) | \(64\) | \(-0.12420\) |
Rank
sage: E.rank()
The elliptic curves in class 480.d have rank \(0\).
Complex multiplication
The elliptic curves in class 480.d do not have complex multiplication.Modular form 480.2.a.d
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.