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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 61446.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61446.cv1 | 61446de2 | \([1, 0, 0, -16743266, -11929605948]\) | \(10593712059133697959507441/4876213982377385856384\) | \(238934485136491906962816\) | \([7]\) | \(6750240\) | \(3.1806\) | |
61446.cv2 | 61446de1 | \([1, 0, 0, -14044626, -20259954786]\) | \(6252564350146719590876401/1254\) | \(61446\) | \([]\) | \(964320\) | \(2.2077\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61446.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 61446.cv do not have complex multiplication.Modular form 61446.2.a.cv
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.