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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 8470.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8470.bg1 | 8470t2 | \([1, 1, 1, -8896, 318979]\) | \(43949604889/42350\) | \(75025608350\) | \([2]\) | \(15360\) | \(1.0079\) | |
| 8470.bg2 | 8470t1 | \([1, 1, 1, -426, 7283]\) | \(-4826809/10780\) | \(-19097427580\) | \([2]\) | \(7680\) | \(0.66136\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8470.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 8470.bg do not have complex multiplication.Modular form 8470.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
