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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 122010a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122010.b2 | 122010a1 | \([1, 1, 0, 30502, -132884142]\) | \(26674615918439/64867662735750\) | \(-7631615653198251750\) | \([]\) | \(2903040\) | \(2.3022\) | \(\Gamma_0(N)\)-optimal |
122010.b1 | 122010a2 | \([1, 1, 0, -274523, 3588847893]\) | \(-19447964478993961/47285712639032280\) | \(-5563116806269508709720\) | \([]\) | \(8709120\) | \(2.8515\) |
Rank
sage: E.rank()
The elliptic curves in class 122010a have rank \(0\).
Complex multiplication
The elliptic curves in class 122010a do not have complex multiplication.Modular form 122010.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.