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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2904.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2904.g1 | 2904k3 | \([0, -1, 0, -57152, -5239188]\) | \(5690357426/891\) | \(3232687822848\) | \([2]\) | \(7680\) | \(1.4114\) | |
2904.g2 | 2904k2 | \([0, -1, 0, -3912, -64260]\) | \(3650692/1089\) | \(1975531447296\) | \([2, 2]\) | \(3840\) | \(1.0648\) | |
2904.g3 | 2904k1 | \([0, -1, 0, -1492, 21892]\) | \(810448/33\) | \(14966147328\) | \([4]\) | \(1920\) | \(0.71821\) | \(\Gamma_0(N)\)-optimal |
2904.g4 | 2904k4 | \([0, -1, 0, 10608, -441780]\) | \(36382894/43923\) | \(-159359536748544\) | \([2]\) | \(7680\) | \(1.4114\) |
Rank
sage: E.rank()
The elliptic curves in class 2904.g have rank \(1\).
Complex multiplication
The elliptic curves in class 2904.g do not have complex multiplication.Modular form 2904.2.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.