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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 190575.ev
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190575.ev1 | 190575er2 | \([0, 0, 1, -729366825, -143336942153969]\) | \(-2126464142970105856/438611057788643355\) | \(-8850814562238138514799937421875\) | \([]\) | \(691200000\) | \(4.6175\) | |
190575.ev2 | 190575er1 | \([0, 0, 1, -243400575, 1711662797281]\) | \(-79028701534867456/16987307596875\) | \(-342790056889287921826171875\) | \([]\) | \(138240000\) | \(3.8127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.ev have rank \(0\).
Complex multiplication
The elliptic curves in class 190575.ev do not have complex multiplication.Modular form 190575.2.a.ev
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.