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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 115920eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.cy1 | 115920eb1 | \([0, 0, 0, -3387, 41834]\) | \(1439069689/579600\) | \(1730676326400\) | \([2]\) | \(147456\) | \(1.0463\) | \(\Gamma_0(N)\)-optimal |
| 115920.cy2 | 115920eb2 | \([0, 0, 0, 11013, 303914]\) | \(49471280711/41992020\) | \(-125387499847680\) | \([2]\) | \(294912\) | \(1.3928\) |
Rank
sage: E.rank()
The elliptic curves in class 115920eb have rank \(0\).
Complex multiplication
The elliptic curves in class 115920eb do not have complex multiplication.Modular form 115920.2.a.eb
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
