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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 63426o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63426.i1 | 63426o1 | \([1, 0, 1, -60083, -778918]\) | \(27027009001/15349092\) | \(13622375650007652\) | \([2]\) | \(1105920\) | \(1.7858\) | \(\Gamma_0(N)\)-optimal |
63426.i2 | 63426o2 | \([1, 0, 1, 237827, -6141298]\) | \(1676253304439/988531038\) | \(-877324935007750878\) | \([2]\) | \(2211840\) | \(2.1323\) |
Rank
sage: E.rank()
The elliptic curves in class 63426o have rank \(1\).
Complex multiplication
The elliptic curves in class 63426o do not have complex multiplication.Modular form 63426.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.