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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 29400q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29400.j4 | 29400q1 | \([0, -1, 0, 10617, -128988]\) | \(4499456/2835\) | \(-83383728750000\) | \([2]\) | \(73728\) | \(1.3602\) | \(\Gamma_0(N)\)-optimal |
| 29400.j3 | 29400q2 | \([0, -1, 0, -44508, -1010988]\) | \(20720464/11025\) | \(5188320900000000\) | \([2, 2]\) | \(147456\) | \(1.7068\) | |
| 29400.j2 | 29400q3 | \([0, -1, 0, -412008, 101154012]\) | \(4108974916/36015\) | \(67794059760000000\) | \([2]\) | \(294912\) | \(2.0534\) | |
| 29400.j1 | 29400q4 | \([0, -1, 0, -559008, -160505988]\) | \(10262905636/13125\) | \(24706290000000000\) | \([2]\) | \(294912\) | \(2.0534\) |
Rank
sage: E.rank()
The elliptic curves in class 29400q have rank \(0\).
Complex multiplication
The elliptic curves in class 29400q do not have complex multiplication.Modular form 29400.2.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.
