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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 270480.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270480.y1 | 270480y4 | \([0, -1, 0, -139026736, -628674667760]\) | \(2466780454987534385284/10072750481768625\) | \(1213490197943907289728000\) | \([2]\) | \(53084160\) | \(3.4771\) | |
270480.y2 | 270480y2 | \([0, -1, 0, -12974236, 881938240]\) | \(8019382352783901136/4629798816890625\) | \(139440947458141476000000\) | \([2, 2]\) | \(26542080\) | \(3.1305\) | |
270480.y3 | 270480y1 | \([0, -1, 0, -9146111, 10622219490]\) | \(44949507773962418176/132895751953125\) | \(250160837144531250000\) | \([2]\) | \(13271040\) | \(2.7839\) | \(\Gamma_0(N)\)-optimal |
270480.y4 | 270480y3 | \([0, -1, 0, 51828264, 6999294240]\) | \(127801365439147434716/74135664409456125\) | \(-8931314464878698137728000\) | \([2]\) | \(53084160\) | \(3.4771\) |
Rank
sage: E.rank()
The elliptic curves in class 270480.y have rank \(0\).
Complex multiplication
The elliptic curves in class 270480.y do not have complex multiplication.Modular form 270480.2.a.y
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.