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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6776.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6776.g1 | 6776c3 | \([0, 0, 0, -36179, -2648690]\) | \(1443468546/7\) | \(25397098496\) | \([2]\) | \(10240\) | \(1.1969\) | |
| 6776.g2 | 6776c4 | \([0, 0, 0, -7139, 183678]\) | \(11090466/2401\) | \(8711204784128\) | \([2]\) | \(10240\) | \(1.1969\) | |
| 6776.g3 | 6776c2 | \([0, 0, 0, -2299, -39930]\) | \(740772/49\) | \(88889844736\) | \([2, 2]\) | \(5120\) | \(0.85034\) | |
| 6776.g4 | 6776c1 | \([0, 0, 0, 121, -2662]\) | \(432/7\) | \(-3174637312\) | \([2]\) | \(2560\) | \(0.50377\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6776.g have rank \(1\).
Complex multiplication
The elliptic curves in class 6776.g do not have complex multiplication.Modular form 6776.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
