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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5304.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5304.g1 | 5304j3 | \([0, -1, 0, -29432, -1933668]\) | \(2753580869496292/39328497\) | \(40272380928\) | \([2]\) | \(10240\) | \(1.1744\) | |
5304.g2 | 5304j2 | \([0, -1, 0, -1892, -27900]\) | \(2927363579728/320445801\) | \(82034125056\) | \([2, 2]\) | \(5120\) | \(0.82778\) | |
5304.g3 | 5304j1 | \([0, -1, 0, -447, 3312]\) | \(618724784128/87947613\) | \(1407161808\) | \([4]\) | \(2560\) | \(0.48121\) | \(\Gamma_0(N)\)-optimal |
5304.g4 | 5304j4 | \([0, -1, 0, 2528, -142820]\) | \(1744147297148/9513325341\) | \(-9741645149184\) | \([2]\) | \(10240\) | \(1.1744\) |
Rank
sage: E.rank()
The elliptic curves in class 5304.g have rank \(0\).
Complex multiplication
The elliptic curves in class 5304.g do not have complex multiplication.Modular form 5304.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.