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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 370260cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
370260.cn1 | 370260cn1 | \([0, 0, 0, -30492, 2048409]\) | \(151732224/85\) | \(1756396437840\) | \([2]\) | \(1075200\) | \(1.2967\) | \(\Gamma_0(N)\)-optimal |
370260.cn2 | 370260cn2 | \([0, 0, 0, -25047, 2803086]\) | \(-5256144/7225\) | \(-2388699155462400\) | \([2]\) | \(2150400\) | \(1.6433\) |
Rank
sage: E.rank()
The elliptic curves in class 370260cn have rank \(0\).
Complex multiplication
The elliptic curves in class 370260cn do not have complex multiplication.Modular form 370260.2.a.cn
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.