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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 145656.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145656.be1 | 145656t4 | \([0, 0, 0, -10488099, -13073542130]\) | \(7080974546692/189\) | \(3405515155854336\) | \([2]\) | \(3932160\) | \(2.4941\) | |
| 145656.be2 | 145656t3 | \([0, 0, 0, -1020459, 47587318]\) | \(6522128932/3720087\) | \(67030754812680895488\) | \([2]\) | \(3932160\) | \(2.4941\) | |
| 145656.be3 | 145656t2 | \([0, 0, 0, -656319, -203742110]\) | \(6940769488/35721\) | \(160910591114117376\) | \([2, 2]\) | \(1966080\) | \(2.1475\) | |
| 145656.be4 | 145656t1 | \([0, 0, 0, -19074, -6578507]\) | \(-2725888/64827\) | \(-18251432788406832\) | \([2]\) | \(983040\) | \(1.8010\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145656.be have rank \(1\).
Complex multiplication
The elliptic curves in class 145656.be do not have complex multiplication.Modular form 145656.2.a.be
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
