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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 3300.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3300.q1 | 3300k2 | \([0, 1, 0, -9908, -382812]\) | \(26894628304/9075\) | \(36300000000\) | \([2]\) | \(4608\) | \(0.99839\) | |
| 3300.q2 | 3300k1 | \([0, 1, 0, -533, -7812]\) | \(-67108864/61875\) | \(-15468750000\) | \([2]\) | \(2304\) | \(0.65181\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3300.q have rank \(1\).
Complex multiplication
The elliptic curves in class 3300.q do not have complex multiplication.Modular form 3300.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
