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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 73920.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.o1 | 73920dy4 | \([0, -1, 0, -136801, -19420415]\) | \(1080077156587801/594247500\) | \(155778416640000\) | \([2]\) | \(393216\) | \(1.6713\) | |
| 73920.o2 | 73920dy2 | \([0, -1, 0, -10081, -184319]\) | \(432252699481/192099600\) | \(50357757542400\) | \([2, 2]\) | \(196608\) | \(1.3248\) | |
| 73920.o3 | 73920dy1 | \([0, -1, 0, -4961, 134145]\) | \(51520374361/887040\) | \(232532213760\) | \([2]\) | \(98304\) | \(0.97820\) | \(\Gamma_0(N)\)-optimal |
| 73920.o4 | 73920dy3 | \([0, -1, 0, 34719, -1411839]\) | \(17655210697319/13448344140\) | \(-3525402726236160\) | \([2]\) | \(393216\) | \(1.6713\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.o have rank \(0\).
Complex multiplication
The elliptic curves in class 73920.o do not have complex multiplication.Modular form 73920.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
