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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 44880ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44880.cv2 | 44880ct1 | \([0, 1, 0, -3200, 58548]\) | \(885012508801/137332800\) | \(562515148800\) | \([2]\) | \(55296\) | \(0.97791\) | \(\Gamma_0(N)\)-optimal |
44880.cv1 | 44880ct2 | \([0, 1, 0, -14080, -589900]\) | \(75370704203521/7497765000\) | \(30710845440000\) | \([2]\) | \(110592\) | \(1.3245\) |
Rank
sage: E.rank()
The elliptic curves in class 44880ct have rank \(1\).
Complex multiplication
The elliptic curves in class 44880ct do not have complex multiplication.Modular form 44880.2.a.ct
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.