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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 250470.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.b1 | 250470b2 | \([1, -1, 0, -264105, -52151225]\) | \(1577505447721/838350\) | \(1082702171811150\) | \([2]\) | \(3225600\) | \(1.8346\) | |
250470.b2 | 250470b1 | \([1, -1, 0, -13635, -1105439]\) | \(-217081801/285660\) | \(-368920740024540\) | \([2]\) | \(1612800\) | \(1.4880\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 250470.b have rank \(0\).
Complex multiplication
The elliptic curves in class 250470.b do not have complex multiplication.Modular form 250470.2.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.