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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 253575.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
253575.cv1 | 253575cv1 | \([0, 0, 1, -235200, 135817281]\) | \(-1073741824/5325075\) | \(-7136109793501171875\) | \([]\) | \(3981312\) | \(2.3021\) | \(\Gamma_0(N)\)-optimal |
253575.cv2 | 253575cv2 | \([0, 0, 1, 2080050, -3324323844]\) | \(742692847616/3992296875\) | \(-5350059638268310546875\) | \([]\) | \(11943936\) | \(2.8514\) |
Rank
sage: E.rank()
The elliptic curves in class 253575.cv have rank \(1\).
Complex multiplication
The elliptic curves in class 253575.cv do not have complex multiplication.Modular form 253575.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.