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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 333270.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333270.g1 | 333270g2 | \([1, -1, 0, -2688351120, 53651387027200]\) | \(1636453355406772967/6914880000\) | \(9079516041943309421760000\) | \([2]\) | \(244187136\) | \(3.9973\) | |
333270.g2 | 333270g1 | \([1, -1, 0, -165402000, 865740948736]\) | \(-381125433207527/26011238400\) | \(-34153804017367159033036800\) | \([2]\) | \(122093568\) | \(3.6507\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333270.g have rank \(1\).
Complex multiplication
The elliptic curves in class 333270.g do not have complex multiplication.Modular form 333270.2.a.g
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.