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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 29575.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29575.o1 | 29575i3 | \([0, -1, 1, -495733, -330943507]\) | \(-178643795968/524596891\) | \(-39564515544544046875\) | \([]\) | \(653184\) | \(2.4473\) | |
29575.o2 | 29575i1 | \([0, -1, 1, -30983, 2113243]\) | \(-43614208/91\) | \(-6863119046875\) | \([]\) | \(72576\) | \(1.3487\) | \(\Gamma_0(N)\)-optimal |
29575.o3 | 29575i2 | \([0, -1, 1, 53517, 10415368]\) | \(224755712/753571\) | \(-56833488827171875\) | \([]\) | \(217728\) | \(1.8980\) |
Rank
sage: E.rank()
The elliptic curves in class 29575.o have rank \(0\).
Complex multiplication
The elliptic curves in class 29575.o do not have complex multiplication.Modular form 29575.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.