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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 35490.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35490.b1 | 35490c1 | \([1, 1, 0, -29342628, 61163851728]\) | \(263469645912923533/10536960000\) | \(111739185713326080000\) | \([2]\) | \(2515968\) | \(2.9299\) | \(\Gamma_0(N)\)-optimal |
| 35490.b2 | 35490c2 | \([1, 1, 0, -27936548, 67291267152]\) | \(-227379752377169293/52942050000000\) | \(-561423936030334650000000\) | \([2]\) | \(5031936\) | \(3.2765\) |
Rank
sage: E.rank()
The elliptic curves in class 35490.b have rank \(0\).
Complex multiplication
The elliptic curves in class 35490.b do not have complex multiplication.Modular form 35490.2.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 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.
