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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 441.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 441.b1 | 441e2 | \([0, 0, 1, -402339, 98307144]\) | \(-1713910976512/1594323\) | \(-6700206067223067\) | \([]\) | \(4368\) | \(1.9596\) | |
| 441.b2 | 441e1 | \([0, 0, 1, -1029, -13806]\) | \(-28672/3\) | \(-12607619787\) | \([]\) | \(336\) | \(0.67717\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 441.b have rank \(0\).
Complex multiplication
The elliptic curves in class 441.b do not have complex multiplication.Modular form 441.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
