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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2280.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2280.i1 | 2280e3 | \([0, 1, 0, -32840, -2301600]\) | \(3825131988299044/961875\) | \(984960000\) | \([2]\) | \(5120\) | \(1.1008\) | |
2280.i2 | 2280e2 | \([0, 1, 0, -2060, -36192]\) | \(3778298043856/59213025\) | \(15158534400\) | \([2, 2]\) | \(2560\) | \(0.75427\) | |
2280.i3 | 2280e1 | \([0, 1, 0, -255, 630]\) | \(115060504576/52780005\) | \(844480080\) | \([4]\) | \(1280\) | \(0.40769\) | \(\Gamma_0(N)\)-optimal |
2280.i4 | 2280e4 | \([0, 1, 0, -160, -98512]\) | \(-445138564/4089438495\) | \(-4187585018880\) | \([2]\) | \(5120\) | \(1.1008\) |
Rank
sage: E.rank()
The elliptic curves in class 2280.i have rank \(0\).
Complex multiplication
The elliptic curves in class 2280.i do not have complex multiplication.Modular form 2280.2.a.i
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.