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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 405720q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405720.q3 | 405720q1 | \([0, 0, 0, -41425051143, -3245209162459558]\) | \(358061097267989271289240144/176126855625\) | \(3867063605986119840000\) | \([2]\) | \(424673280\) | \(4.3794\) | \(\Gamma_0(N)\)-optimal* |
405720.q2 | 405720q2 | \([0, 0, 0, -41425271643, -3245172887431258]\) | \(89516703758060574923008036/1985322833430374025\) | \(174360000876597558992288793600\) | \([2, 2]\) | \(849346560\) | \(4.7260\) | \(\Gamma_0(N)\)-optimal* |
405720.q1 | 405720q3 | \([0, 0, 0, -42907649043, -3000431489264818]\) | \(49737293673675178002921218/6641736806881023047235\) | \(1166614533384420260398992845690880\) | \([2]\) | \(1698693120\) | \(5.0726\) | \(\Gamma_0(N)\)-optimal* |
405720.q4 | 405720q4 | \([0, 0, 0, -39946422243, -3487592683786498]\) | \(-40133926989810174413190818/6689384645060302103835\) | \(-1174983829265989473349769572423680\) | \([2]\) | \(1698693120\) | \(5.0726\) |
Rank
sage: E.rank()
The elliptic curves in class 405720q have rank \(0\).
Complex multiplication
The elliptic curves in class 405720q do not have complex multiplication.Modular form 405720.2.a.q
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.