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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 70805bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70805.bm2 | 70805bg1 | \([1, -1, 0, 122771, 34567728]\) | \(24718462497/76765625\) | \(-635556900601109375\) | \([2]\) | \(663552\) | \(2.0994\) | \(\Gamma_0(N)\)-optimal |
| 70805.bm1 | 70805bg2 | \([1, -1, 0, -1141604, 403512353]\) | \(19873882747503/3017196125\) | \(24979928421226002875\) | \([2]\) | \(1327104\) | \(2.4459\) |
Rank
sage: E.rank()
The elliptic curves in class 70805bg have rank \(1\).
Complex multiplication
The elliptic curves in class 70805bg do not have complex multiplication.Modular form 70805.2.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 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.
