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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 265200g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
265200.g3 | 265200g1 | \([0, -1, 0, -1292008, -311097488]\) | \(3726830856733921/1501644718080\) | \(96105261957120000000\) | \([2]\) | \(10616832\) | \(2.5323\) | \(\Gamma_0(N)\)-optimal |
265200.g2 | 265200g2 | \([0, -1, 0, -9484008, 11026630512]\) | \(1474074790091785441/32813650022400\) | \(2100073601433600000000\) | \([2, 2]\) | \(21233664\) | \(2.8789\) | |
265200.g1 | 265200g3 | \([0, -1, 0, -150924008, 713700550512]\) | \(5940441603429810927841/3044264109120\) | \(194832902983680000000\) | \([2]\) | \(42467328\) | \(3.2254\) | |
265200.g4 | 265200g4 | \([0, -1, 0, 883992, 33836230512]\) | \(1193680917131039/7728836230440000\) | \(-494645518748160000000000\) | \([2]\) | \(42467328\) | \(3.2254\) |
Rank
sage: E.rank()
The elliptic curves in class 265200g have rank \(0\).
Complex multiplication
The elliptic curves in class 265200g do not have complex multiplication.Modular form 265200.2.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.