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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 6300.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6300.n1 | 6300w2 | \([0, 0, 0, -519735, 144170350]\) | \(665567485783184/257298363\) | \(6002256212064000\) | \([2]\) | \(64512\) | \(1.9930\) | |
| 6300.n2 | 6300w1 | \([0, 0, 0, -27660, 2944825]\) | \(-1605176213504/1640558367\) | \(-2391934099086000\) | \([2]\) | \(32256\) | \(1.6464\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6300.n have rank \(0\).
Complex multiplication
The elliptic curves in class 6300.n do not have complex multiplication.Modular form 6300.2.a.n
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.
