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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 92400b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.o4 | 92400b1 | \([0, -1, 0, 9092, -322688]\) | \(20777545136/23059575\) | \(-92238300000000\) | \([2]\) | \(196608\) | \(1.3661\) | \(\Gamma_0(N)\)-optimal |
| 92400.o3 | 92400b2 | \([0, -1, 0, -51408, -2984688]\) | \(939083699236/300155625\) | \(4802490000000000\) | \([2, 2]\) | \(393216\) | \(1.7127\) | |
| 92400.o2 | 92400b3 | \([0, -1, 0, -326408, 69615312]\) | \(120186986927618/4332064275\) | \(138626056800000000\) | \([2]\) | \(786432\) | \(2.0593\) | |
| 92400.o1 | 92400b4 | \([0, -1, 0, -744408, -246920688]\) | \(1425631925916578/270703125\) | \(8662500000000000\) | \([2]\) | \(786432\) | \(2.0593\) |
Rank
sage: E.rank()
The elliptic curves in class 92400b have rank \(1\).
Complex multiplication
The elliptic curves in class 92400b do not have complex multiplication.Modular form 92400.2.a.b
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.
