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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 68970.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68970.q1 | 68970i1 | \([1, 1, 0, -256962, 50029236]\) | \(1409791893399845171/1795089600\) | \(2389264257600\) | \([2]\) | \(668160\) | \(1.6533\) | \(\Gamma_0(N)\)-optimal |
68970.q2 | 68970i2 | \([1, 1, 0, -254762, 50930796]\) | \(-1373890970207112371/50349166750440\) | \(-67014740944835640\) | \([2]\) | \(1336320\) | \(1.9998\) |
Rank
sage: E.rank()
The elliptic curves in class 68970.q have rank \(0\).
Complex multiplication
The elliptic curves in class 68970.q do not have complex multiplication.Modular form 68970.2.a.q
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.