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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 162450.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.eb1 | 162450bf1 | \([1, -1, 1, -8105, 325397]\) | \(-14317849/2700\) | \(-11102442187500\) | \([]\) | \(497664\) | \(1.2273\) | \(\Gamma_0(N)\)-optimal |
| 162450.eb2 | 162450bf2 | \([1, -1, 1, 56020, -1598353]\) | \(4728305591/3000000\) | \(-12336046875000000\) | \([]\) | \(1492992\) | \(1.7766\) |
Rank
sage: E.rank()
The elliptic curves in class 162450.eb have rank \(0\).
Complex multiplication
The elliptic curves in class 162450.eb do not have complex multiplication.Modular form 162450.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
