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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 126075be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126075.bg1 | 126075be1 | \([0, 1, 1, -14008, -658781]\) | \(-102400/3\) | \(-8906445451875\) | \([]\) | \(408000\) | \(1.2637\) | \(\Gamma_0(N)\)-optimal |
| 126075.bg2 | 126075be2 | \([0, 1, 1, 70042, 31532369]\) | \(20480/243\) | \(-450888801001171875\) | \([]\) | \(2040000\) | \(2.0684\) |
Rank
sage: E.rank()
The elliptic curves in class 126075be have rank \(1\).
Complex multiplication
The elliptic curves in class 126075be do not have complex multiplication.Modular form 126075.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
