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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3300.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3300.b1 | 3300e4 | \([0, -1, 0, -6249908, -6011849688]\) | \(6749703004355978704/5671875\) | \(22687500000000\) | \([2]\) | \(41472\) | \(2.2983\) | |
| 3300.b2 | 3300e3 | \([0, -1, 0, -390533, -93880938]\) | \(-26348629355659264/24169921875\) | \(-6042480468750000\) | \([2]\) | \(20736\) | \(1.9517\) | |
| 3300.b3 | 3300e2 | \([0, -1, 0, -78908, -7829688]\) | \(13584145739344/1195803675\) | \(4783214700000000\) | \([2]\) | \(13824\) | \(1.7490\) | |
| 3300.b4 | 3300e1 | \([0, -1, 0, 5467, -573438]\) | \(72268906496/606436875\) | \(-151609218750000\) | \([2]\) | \(6912\) | \(1.4024\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3300.b have rank \(1\).
Complex multiplication
The elliptic curves in class 3300.b do not have complex multiplication.Modular form 3300.2.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.
