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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 72450.eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72450.eo1 | 72450em1 | \([1, -1, 1, -242599730, -1454338353103]\) | \(138626767243242683688529/5300196249600\) | \(60372547905600000000\) | \([2]\) | \(8847360\) | \(3.2868\) | \(\Gamma_0(N)\)-optimal |
72450.eo2 | 72450em2 | \([1, -1, 1, -242239730, -1458870033103]\) | \(-138010547060620856386129/857302254769101120\) | \(-9765208495729292445000000\) | \([2]\) | \(17694720\) | \(3.6334\) |
Rank
sage: E.rank()
The elliptic curves in class 72450.eo have rank \(1\).
Complex multiplication
The elliptic curves in class 72450.eo do not have complex multiplication.Modular form 72450.2.a.eo
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.