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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 30400.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30400.by1 | 30400bh2 | \([0, -1, 0, -41666033, 103533193937]\) | \(31248575021659890256/28203125\) | \(7220000000000000\) | \([2]\) | \(1720320\) | \(2.7738\) | |
30400.by2 | 30400bh1 | \([0, -1, 0, -2603533, 1619131437]\) | \(-121981271658244096/115966796875\) | \(-1855468750000000000\) | \([2]\) | \(860160\) | \(2.4273\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30400.by have rank \(0\).
Complex multiplication
The elliptic curves in class 30400.by do not have complex multiplication.Modular form 30400.2.a.by
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.