Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 54760.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54760.e1 | 54760c4 | \([0, 0, 0, -146483, -21578178]\) | \(132304644/5\) | \(13136519214080\) | \([2]\) | \(202752\) | \(1.6032\) | |
54760.e2 | 54760c2 | \([0, 0, 0, -9583, -303918]\) | \(148176/25\) | \(16420649017600\) | \([2, 2]\) | \(101376\) | \(1.2567\) | |
54760.e3 | 54760c1 | \([0, 0, 0, -2738, 50653]\) | \(55296/5\) | \(205258112720\) | \([2]\) | \(50688\) | \(0.91010\) | \(\Gamma_0(N)\)-optimal |
54760.e4 | 54760c3 | \([0, 0, 0, 17797, -1722202]\) | \(237276/625\) | \(-1642064901760000\) | \([2]\) | \(202752\) | \(1.6032\) |
Rank
sage: E.rank()
The elliptic curves in class 54760.e have rank \(0\).
Complex multiplication
The elliptic curves in class 54760.e do not have complex multiplication.Modular form 54760.2.a.e
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.