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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 47190.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.b1 | 47190f2 | \([1, 1, 0, -1952061663, 33195389531517]\) | \(464352938845529653759213009/2445173327025000\) | \(4331773704397736025000\) | \([2]\) | \(19353600\) | \(3.7684\) | |
47190.b2 | 47190f1 | \([1, 1, 0, -121936663, 519239706517]\) | \(-113180217375258301213009/260161419375000000\) | \(-460891824269394375000000\) | \([2]\) | \(9676800\) | \(3.4219\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47190.b have rank \(1\).
Complex multiplication
The elliptic curves in class 47190.b do not have complex multiplication.Modular form 47190.2.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.