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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 152592.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.cq1 | 152592cv1 | \([0, 1, 0, -2408, -14268]\) | \(62500/33\) | \(815656731648\) | \([2]\) | \(163840\) | \(0.97716\) | \(\Gamma_0(N)\)-optimal |
152592.cq2 | 152592cv2 | \([0, 1, 0, 9152, -102124]\) | \(1714750/1089\) | \(-53833344288768\) | \([2]\) | \(327680\) | \(1.3237\) |
Rank
sage: E.rank()
The elliptic curves in class 152592.cq have rank \(1\).
Complex multiplication
The elliptic curves in class 152592.cq do not have complex multiplication.Modular form 152592.2.a.cq
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.