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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 7350.cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.cr1 | 7350cv2 | \([1, 0, 0, -7568, -222048]\) | \(1118063669939/153055008\) | \(6562233468000\) | \([2]\) | \(17920\) | \(1.1863\) | |
7350.cr2 | 7350cv1 | \([1, 0, 0, -1968, 29952]\) | \(19661138099/2239488\) | \(96018048000\) | \([2]\) | \(8960\) | \(0.83970\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7350.cr have rank \(1\).
Complex multiplication
The elliptic curves in class 7350.cr do not have complex multiplication.Modular form 7350.2.a.cr
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.