Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 11550.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11550.b1 | 11550a4 | \([1, 1, 0, -353325, -80978625]\) | \(312196988566716625/25367712678\) | \(396370510593750\) | \([2]\) | \(82944\) | \(1.8463\) | |
11550.b2 | 11550a3 | \([1, 1, 0, -20575, -1451375]\) | \(-61653281712625/21875235228\) | \(-341800550437500\) | \([2]\) | \(41472\) | \(1.4997\) | |
11550.b3 | 11550a2 | \([1, 1, 0, -9075, 163125]\) | \(5290763640625/2291573592\) | \(35805837375000\) | \([2]\) | \(27648\) | \(1.2970\) | |
11550.b4 | 11550a1 | \([1, 1, 0, 1925, 20125]\) | \(50447927375/39517632\) | \(-617463000000\) | \([2]\) | \(13824\) | \(0.95040\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.b have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.b do not have complex multiplication.Modular form 11550.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.