Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 48552.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48552.q1 | 48552c4 | \([0, -1, 0, -157312, -21774020]\) | \(17418812548/1753941\) | \(43351932835255296\) | \([2]\) | \(368640\) | \(1.9285\) | |
48552.q2 | 48552c2 | \([0, -1, 0, -35932, 2259220]\) | \(830321872/127449\) | \(787535112059136\) | \([2, 2]\) | \(184320\) | \(1.5819\) | |
48552.q3 | 48552c1 | \([0, -1, 0, -34487, 2476548]\) | \(11745974272/357\) | \(137873794128\) | \([4]\) | \(92160\) | \(1.2353\) | \(\Gamma_0(N)\)-optimal |
48552.q4 | 48552c3 | \([0, -1, 0, 62328, 12360348]\) | \(1083360092/3306177\) | \(-81718349274842112\) | \([2]\) | \(368640\) | \(1.9285\) |
Rank
sage: E.rank()
The elliptic curves in class 48552.q have rank \(1\).
Complex multiplication
The elliptic curves in class 48552.q do not have complex multiplication.Modular form 48552.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.