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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 34320.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34320.g1 | 34320be4 | \([0, -1, 0, -2566816, 1583670016]\) | \(456612868287073618849/12544848030000\) | \(51383697530880000\) | \([4]\) | \(589824\) | \(2.3099\) | |
| 34320.g2 | 34320be3 | \([0, -1, 0, -715936, -210556160]\) | \(9908022260084596129/1047363281250000\) | \(4290000000000000000\) | \([2]\) | \(589824\) | \(2.3099\) | |
| 34320.g3 | 34320be2 | \([0, -1, 0, -166816, 22710016]\) | \(125337052492018849/18404100000000\) | \(75383193600000000\) | \([2, 2]\) | \(294912\) | \(1.9633\) | |
| 34320.g4 | 34320be1 | \([0, -1, 0, 17504, 1918720]\) | \(144794100308831/474439680000\) | \(-1943304929280000\) | \([2]\) | \(147456\) | \(1.6167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34320.g have rank \(0\).
Complex multiplication
The elliptic curves in class 34320.g do not have complex multiplication.Modular form 34320.2.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.
