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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 145200.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145200.o1 | 145200eu4 | \([0, -1, 0, -88712651408, -10169425563866688]\) | \(680995599504466943307169/52207031250000000\) | \(5919228191250000000000000000000\) | \([2]\) | \(619315200\) | \(4.9529\) | |
145200.o2 | 145200eu2 | \([0, -1, 0, -5913803408, -136523554010688]\) | \(201738262891771037089/45727545600000000\) | \(5184584730283622400000000000000\) | \([2, 2]\) | \(309657600\) | \(4.6063\) | |
145200.o3 | 145200eu1 | \([0, -1, 0, -1948875408, 31288058661312]\) | \(7220044159551112609/448454983680000\) | \(50845782997959966720000000000\) | \([2]\) | \(154828800\) | \(4.2597\) | \(\Gamma_0(N)\)-optimal |
145200.o4 | 145200eu3 | \([0, -1, 0, 13446196592, -843628194010688]\) | \(2371297246710590562911/4084000833203280000\) | \(-463043622404507898885120000000000\) | \([2]\) | \(619315200\) | \(4.9529\) |
Rank
sage: E.rank()
The elliptic curves in class 145200.o have rank \(1\).
Complex multiplication
The elliptic curves in class 145200.o do not have complex multiplication.Modular form 145200.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.