Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 480g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480.g3 | 480g1 | \([0, 1, 0, -10, 8]\) | \(1906624/225\) | \(14400\) | \([2, 2]\) | \(32\) | \(-0.47077\) | \(\Gamma_0(N)\)-optimal |
480.g2 | 480g2 | \([0, 1, 0, -40, -100]\) | \(14172488/1875\) | \(960000\) | \([2]\) | \(64\) | \(-0.12420\) | |
480.g1 | 480g3 | \([0, 1, 0, -160, 728]\) | \(890277128/15\) | \(7680\) | \([2]\) | \(64\) | \(-0.12420\) | |
480.g4 | 480g4 | \([0, 1, 0, 15, 63]\) | \(85184/405\) | \(-1658880\) | \([4]\) | \(64\) | \(-0.12420\) |
Rank
sage: E.rank()
The elliptic curves in class 480g have rank \(0\).
Complex multiplication
The elliptic curves in class 480g do not have complex multiplication.Modular form 480.2.a.g
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.