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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 37570b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37570.d2 | 37570b1 | \([1, 1, 0, -9398, 344708]\) | \(3803721481/26000\) | \(627576794000\) | \([2]\) | \(110592\) | \(1.0977\) | \(\Gamma_0(N)\)-optimal |
37570.d3 | 37570b2 | \([1, 1, 0, -3618, 771272]\) | \(-217081801/10562500\) | \(-254953072562500\) | \([2]\) | \(221184\) | \(1.4443\) | |
37570.d1 | 37570b3 | \([1, 1, 0, -59973, -5451187]\) | \(988345570681/44994560\) | \(1086059296624640\) | \([2]\) | \(331776\) | \(1.6471\) | |
37570.d4 | 37570b4 | \([1, 1, 0, 32507, -20636403]\) | \(157376536199/7722894400\) | \(-186411896459713600\) | \([2]\) | \(663552\) | \(1.9936\) |
Rank
sage: E.rank()
The elliptic curves in class 37570b have rank \(0\).
Complex multiplication
The elliptic curves in class 37570b do not have complex multiplication.Modular form 37570.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.