Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1100.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1100.e1 | 1100b4 | \([0, -1, 0, -177508, -28726488]\) | \(154639330142416/33275\) | \(133100000000\) | \([2]\) | \(5184\) | \(1.5192\) | |
1100.e2 | 1100b3 | \([0, -1, 0, -11133, -442738]\) | \(610462990336/8857805\) | \(2214451250000\) | \([2]\) | \(2592\) | \(1.1726\) | |
1100.e3 | 1100b2 | \([0, -1, 0, -2508, -26488]\) | \(436334416/171875\) | \(687500000000\) | \([2]\) | \(1728\) | \(0.96986\) | |
1100.e4 | 1100b1 | \([0, -1, 0, -1133, 14762]\) | \(643956736/15125\) | \(3781250000\) | \([2]\) | \(864\) | \(0.62329\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1100.e have rank \(0\).
Complex multiplication
The elliptic curves in class 1100.e do not have complex multiplication.Modular form 1100.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.