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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 53371.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53371.b1 | 53371a3 | \([0, -1, 1, -2161057, -1222057453]\) | \(-50357871050752/19\) | \(-421122861451\) | \([]\) | \(432432\) | \(2.0186\) | |
| 53371.b2 | 53371a2 | \([0, -1, 1, -26217, -1729538]\) | \(-89915392/6859\) | \(-152025352983811\) | \([]\) | \(144144\) | \(1.4693\) | |
| 53371.b3 | 53371a1 | \([0, -1, 1, 1873, -2003]\) | \(32768/19\) | \(-421122861451\) | \([]\) | \(48048\) | \(0.91997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53371.b have rank \(1\).
Complex multiplication
The elliptic curves in class 53371.b do not have complex multiplication.Modular form 53371.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
