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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 277440.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277440.bc1 | 277440bc3 | \([0, -1, 0, -65121, 6359841]\) | \(38614472/405\) | \(320330643701760\) | \([2]\) | \(1310720\) | \(1.5999\) | |
| 277440.bc2 | 277440bc2 | \([0, -1, 0, -7321, -79079]\) | \(438976/225\) | \(22245183590400\) | \([2, 2]\) | \(655360\) | \(1.2533\) | |
| 277440.bc3 | 277440bc1 | \([0, -1, 0, -5876, -171270]\) | \(14526784/15\) | \(23172066240\) | \([2]\) | \(327680\) | \(0.90676\) | \(\Gamma_0(N)\)-optimal |
| 277440.bc4 | 277440bc4 | \([0, -1, 0, 27359, -640895]\) | \(2863288/1875\) | \(-1483012239360000\) | \([2]\) | \(1310720\) | \(1.5999\) |
Rank
sage: E.rank()
The elliptic curves in class 277440.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 277440.bc do not have complex multiplication.Modular form 277440.2.a.bc
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.
