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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 12480o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12480.bj3 | 12480o1 | \([0, -1, 0, -260, -1530]\) | \(30488290624/195\) | \(12480\) | \([2]\) | \(1536\) | \(-0.029371\) | \(\Gamma_0(N)\)-optimal |
12480.bj2 | 12480o2 | \([0, -1, 0, -265, -1463]\) | \(504358336/38025\) | \(155750400\) | \([2, 2]\) | \(3072\) | \(0.31720\) | |
12480.bj1 | 12480o3 | \([0, -1, 0, -865, 8257]\) | \(2186875592/428415\) | \(14038302720\) | \([4]\) | \(6144\) | \(0.66378\) | |
12480.bj4 | 12480o4 | \([0, -1, 0, 255, -6975]\) | \(55742968/658125\) | \(-21565440000\) | \([2]\) | \(6144\) | \(0.66378\) |
Rank
sage: E.rank()
The elliptic curves in class 12480o have rank \(1\).
Complex multiplication
The elliptic curves in class 12480o do not have complex multiplication.Modular form 12480.2.a.o
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.