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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 46090.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46090.e1 | 46090d4 | \([1, -1, 0, -210164, -36994160]\) | \(1026596670815958818841/1193414857997120\) | \(1193414857997120\) | \([2]\) | \(433152\) | \(1.8053\) | |
46090.e2 | 46090d3 | \([1, -1, 0, -150644, 22357008]\) | \(378077515421828519961/3592654845560000\) | \(3592654845560000\) | \([4]\) | \(433152\) | \(1.8053\) | |
46090.e3 | 46090d2 | \([1, -1, 0, -16564, -248880]\) | \(502613472723516441/263207792742400\) | \(263207792742400\) | \([2, 2]\) | \(216576\) | \(1.4587\) | |
46090.e4 | 46090d1 | \([1, -1, 0, 3916, -31792]\) | \(6640325636015079/4252940369920\) | \(-4252940369920\) | \([2]\) | \(108288\) | \(1.1122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46090.e have rank \(1\).
Complex multiplication
The elliptic curves in class 46090.e do not have complex multiplication.Modular form 46090.2.a.e
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.