Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 348480g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348480.g4 | 348480g1 | \([0, 0, 0, 15972, -362032]\) | \(21296/15\) | \(-317391168061440\) | \([2]\) | \(1474560\) | \(1.4711\) | \(\Gamma_0(N)\)-optimal |
348480.g3 | 348480g2 | \([0, 0, 0, -71148, -3045328]\) | \(470596/225\) | \(19043470083686400\) | \([2, 2]\) | \(2949120\) | \(1.8177\) | |
348480.g2 | 348480g3 | \([0, 0, 0, -593868, 174052208]\) | \(136835858/1875\) | \(317391168061440000\) | \([2]\) | \(5898240\) | \(2.1642\) | |
348480.g1 | 348480g4 | \([0, 0, 0, -942348, -351873808]\) | \(546718898/405\) | \(68556492301271040\) | \([2]\) | \(5898240\) | \(2.1642\) |
Rank
sage: E.rank()
The elliptic curves in class 348480g have rank \(1\).
Complex multiplication
The elliptic curves in class 348480g do not have complex multiplication.Modular form 348480.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.