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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 87120.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
87120.cx1 | 87120bi4 | \([0, 0, 0, -11500203, 15010887562]\) | \(127191074376964/495\) | \(654619284126720\) | \([2]\) | \(1966080\) | \(2.4791\) | |
87120.cx2 | 87120bi2 | \([0, 0, 0, -719103, 234311902]\) | \(124386546256/245025\) | \(81009136410681600\) | \([2, 2]\) | \(983040\) | \(2.1325\) | |
87120.cx3 | 87120bi3 | \([0, 0, 0, -479523, 392961778]\) | \(-9220796644/45106875\) | \(-59652182266047360000\) | \([2]\) | \(1966080\) | \(2.4791\) | |
87120.cx4 | 87120bi1 | \([0, 0, 0, -60258, 949003]\) | \(1171019776/658845\) | \(13614035424572880\) | \([2]\) | \(491520\) | \(1.7859\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.cx do not have complex multiplication.Modular form 87120.2.a.cx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.