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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 90160ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90160.ca4 | 90160ba1 | \([0, 0, 0, 1078, 31899]\) | \(73598976/276115\) | \(-519754458160\) | \([2]\) | \(61440\) | \(0.93088\) | \(\Gamma_0(N)\)-optimal |
| 90160.ca3 | 90160ba2 | \([0, 0, 0, -10927, 384846]\) | \(4790692944/648025\) | \(19517310265600\) | \([2, 2]\) | \(122880\) | \(1.2775\) | |
| 90160.ca2 | 90160ba3 | \([0, 0, 0, -45227, -3312694]\) | \(84923690436/9794435\) | \(1179960814914560\) | \([2]\) | \(245760\) | \(1.6240\) | |
| 90160.ca1 | 90160ba4 | \([0, 0, 0, -168707, 26670994]\) | \(4407931365156/100625\) | \(12122552960000\) | \([4]\) | \(245760\) | \(1.6240\) |
Rank
sage: E.rank()
The elliptic curves in class 90160ba have rank \(1\).
Complex multiplication
The elliptic curves in class 90160ba do not have complex multiplication.Modular form 90160.2.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.
