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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 88935bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.q4 | 88935bi1 | \([1, 1, 1, -20875, -8435008]\) | \(-4826809/144375\) | \(-30090981125349375\) | \([4]\) | \(552960\) | \(1.8423\) | \(\Gamma_0(N)\)-optimal |
88935.q3 | 88935bi2 | \([1, 1, 1, -762000, -255081408]\) | \(234770924809/1334025\) | \(278040665598228225\) | \([2, 2]\) | \(1105920\) | \(2.1889\) | |
88935.q2 | 88935bi3 | \([1, 1, 1, -1206675, 76290402]\) | \(932288503609/527295615\) | \(109900207088793009735\) | \([2]\) | \(2211840\) | \(2.5355\) | |
88935.q1 | 88935bi4 | \([1, 1, 1, -12175325, -16357000318]\) | \(957681397954009/31185\) | \(6499651923075465\) | \([2]\) | \(2211840\) | \(2.5355\) |
Rank
sage: E.rank()
The elliptic curves in class 88935bi have rank \(0\).
Complex multiplication
The elliptic curves in class 88935bi do not have complex multiplication.Modular form 88935.2.a.bi
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.