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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 930.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
930.o1 | 930o5 | \([1, 0, 0, -307520, -65664060]\) | \(3216206300355197383681/57660\) | \(57660\) | \([2]\) | \(4096\) | \(1.3818\) | |
930.o2 | 930o3 | \([1, 0, 0, -19220, -1027200]\) | \(785209010066844481/3324675600\) | \(3324675600\) | \([2, 2]\) | \(2048\) | \(1.0353\) | |
930.o3 | 930o6 | \([1, 0, 0, -18920, -1060740]\) | \(-749011598724977281/51173462246460\) | \(-51173462246460\) | \([2]\) | \(4096\) | \(1.3818\) | |
930.o4 | 930o4 | \([1, 0, 0, -3700, 67232]\) | \(5601911201812801/1271193750000\) | \(1271193750000\) | \([8]\) | \(2048\) | \(1.0353\) | |
930.o5 | 930o2 | \([1, 0, 0, -1220, -15600]\) | \(200828550012481/12454560000\) | \(12454560000\) | \([2, 4]\) | \(1024\) | \(0.68868\) | |
930.o6 | 930o1 | \([1, 0, 0, 60, -1008]\) | \(23862997439/457113600\) | \(-457113600\) | \([4]\) | \(512\) | \(0.34210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 930.o have rank \(0\).
Complex multiplication
The elliptic curves in class 930.o do not have complex multiplication.Modular form 930.2.a.o
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.