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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 504g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 504.e4 | 504g1 | \([0, 0, 0, -66, -1339]\) | \(-2725888/64827\) | \(-756142128\) | \([4]\) | \(192\) | \(0.38435\) | \(\Gamma_0(N)\)-optimal |
| 504.e3 | 504g2 | \([0, 0, 0, -2271, -41470]\) | \(6940769488/35721\) | \(6666395904\) | \([2, 2]\) | \(384\) | \(0.73092\) | |
| 504.e1 | 504g3 | \([0, 0, 0, -36291, -2661010]\) | \(7080974546692/189\) | \(141087744\) | \([2]\) | \(768\) | \(1.0775\) | |
| 504.e2 | 504g4 | \([0, 0, 0, -3531, 9686]\) | \(6522128932/3720087\) | \(2777030065152\) | \([2]\) | \(768\) | \(1.0775\) |
Rank
sage: E.rank()
The elliptic curves in class 504g have rank \(0\).
Complex multiplication
The elliptic curves in class 504g do not have complex multiplication.Modular form 504.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
