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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 254320ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254320.ba3 | 254320ba1 | \([0, 0, 0, -1457138, -677016313]\) | \(885956203616256/15125\) | \(5841291698000\) | \([2]\) | \(2654208\) | \(1.9916\) | \(\Gamma_0(N)\)-optimal |
| 254320.ba2 | 254320ba2 | \([0, 0, 0, -1458583, -675606282]\) | \(55537159171536/228765625\) | \(1413592590916000000\) | \([2, 2]\) | \(5308416\) | \(2.3381\) | |
| 254320.ba1 | 254320ba3 | \([0, 0, 0, -2181083, 63800218]\) | \(46424454082884/26794860125\) | \(662285091955236992000\) | \([2]\) | \(10616832\) | \(2.6847\) | |
| 254320.ba4 | 254320ba4 | \([0, 0, 0, -759203, -1324770798]\) | \(-1957960715364/29541015625\) | \(-730161462250000000000\) | \([2]\) | \(10616832\) | \(2.6847\) |
Rank
sage: E.rank()
The elliptic curves in class 254320ba have rank \(1\).
Complex multiplication
The elliptic curves in class 254320ba do not have complex multiplication.Modular form 254320.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
