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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 2790.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2790.bc1 | 2790bb3 | \([1, -1, 1, -13622, 588971]\) | \(383432500775449/18701300250\) | \(13633247882250\) | \([2]\) | \(9216\) | \(1.2799\) | |
2790.bc2 | 2790bb2 | \([1, -1, 1, -2372, -32029]\) | \(2023804595449/540562500\) | \(394070062500\) | \([2, 2]\) | \(4608\) | \(0.93332\) | |
2790.bc3 | 2790bb1 | \([1, -1, 1, -2192, -38941]\) | \(1597099875769/186000\) | \(135594000\) | \([2]\) | \(2304\) | \(0.58674\) | \(\Gamma_0(N)\)-optimal |
2790.bc4 | 2790bb4 | \([1, -1, 1, 5998, -212821]\) | \(32740359775271/45410156250\) | \(-33104003906250\) | \([2]\) | \(9216\) | \(1.2799\) |
Rank
sage: E.rank()
The elliptic curves in class 2790.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 2790.bc do not have complex multiplication.Modular form 2790.2.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.