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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 148225.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148225.cb1 | 148225cb3 | \([1, -1, 0, -8773067, 10001335966]\) | \(22930509321/6875\) | \(22389122861123046875\) | \([2]\) | \(4423680\) | \(2.6910\) | |
148225.cb2 | 148225cb4 | \([1, -1, 0, -4326317, -3381899284]\) | \(2749884201/73205\) | \(238399380225238203125\) | \([2]\) | \(4423680\) | \(2.6910\) | |
148225.cb3 | 148225cb2 | \([1, -1, 0, -620692, 112505091]\) | \(8120601/3025\) | \(9851214058894140625\) | \([2, 2]\) | \(2211840\) | \(2.3444\) | |
148225.cb4 | 148225cb1 | \([1, -1, 0, 120433, 12453216]\) | \(59319/55\) | \(-179112982888984375\) | \([2]\) | \(1105920\) | \(1.9978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148225.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 148225.cb do not have complex multiplication.Modular form 148225.2.a.cb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.