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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 161448bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161448.n3 | 161448bj1 | \([0, -1, 0, -7047, 228540]\) | \(2725888/21\) | \(298201236816\) | \([2]\) | \(230400\) | \(1.0308\) | \(\Gamma_0(N)\)-optimal |
161448.n2 | 161448bj2 | \([0, -1, 0, -11852, -117420]\) | \(810448/441\) | \(100195615570176\) | \([2, 2]\) | \(460800\) | \(1.3774\) | |
161448.n4 | 161448bj3 | \([0, -1, 0, 45808, -970788]\) | \(11696828/7203\) | \(-6546113550584832\) | \([2]\) | \(921600\) | \(1.7240\) | |
161448.n1 | 161448bj4 | \([0, -1, 0, -146392, -21482372]\) | \(381775972/567\) | \(515291737218048\) | \([2]\) | \(921600\) | \(1.7240\) |
Rank
sage: E.rank()
The elliptic curves in class 161448bj have rank \(0\).
Complex multiplication
The elliptic curves in class 161448bj do not have complex multiplication.Modular form 161448.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.