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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 85800g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85800.ba4 | 85800g1 | \([0, -1, 0, 617, 40012]\) | \(103737344/2854995\) | \(-713748750000\) | \([4]\) | \(98304\) | \(0.95458\) | \(\Gamma_0(N)\)-optimal |
| 85800.ba3 | 85800g2 | \([0, -1, 0, -14508, 645012]\) | \(84433792336/4601025\) | \(18404100000000\) | \([2, 2]\) | \(196608\) | \(1.3012\) | |
| 85800.ba2 | 85800g3 | \([0, -1, 0, -42008, -2489988]\) | \(512401135684/127239255\) | \(2035828080000000\) | \([2]\) | \(393216\) | \(1.6477\) | |
| 85800.ba1 | 85800g4 | \([0, -1, 0, -229008, 42258012]\) | \(83015194102564/268125\) | \(4290000000000\) | \([2]\) | \(393216\) | \(1.6477\) |
Rank
sage: E.rank()
The elliptic curves in class 85800g have rank \(1\).
Complex multiplication
The elliptic curves in class 85800g do not have complex multiplication.Modular form 85800.2.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.
