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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 42050.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42050.y1 | 42050u2 | \([1, 1, 1, -9566813, -11470566969]\) | \(-10418796526321/82044596\) | \(-762531860356614312500\) | \([]\) | \(2352000\) | \(2.8355\) | |
42050.y2 | 42050u1 | \([1, 1, 1, 104687, 21698031]\) | \(13651919/29696\) | \(-275998020944000000\) | \([]\) | \(470400\) | \(2.0308\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 42050.y have rank \(0\).
Complex multiplication
The elliptic curves in class 42050.y do not have complex multiplication.Modular form 42050.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.