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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1380.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1380.b1 | 1380a1 | \([0, -1, 0, -21, -30]\) | \(67108864/1725\) | \(27600\) | \([2]\) | \(120\) | \(-0.36567\) | \(\Gamma_0(N)\)-optimal |
1380.b2 | 1380a2 | \([0, -1, 0, 4, -120]\) | \(21296/23805\) | \(-6094080\) | \([2]\) | \(240\) | \(-0.019099\) |
Rank
sage: E.rank()
The elliptic curves in class 1380.b have rank \(0\).
Complex multiplication
The elliptic curves in class 1380.b do not have complex multiplication.Modular form 1380.2.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.