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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 1554n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1554.l2 | 1554n1 | \([1, 0, 0, -4767, 127449]\) | \(-11980221891814513/127896039936\) | \(-127896039936\) | \([9]\) | \(3888\) | \(0.94763\) | \(\Gamma_0(N)\)-optimal |
1554.l3 | 1554n2 | \([1, 0, 0, 15753, 666801]\) | \(432326451325256207/441510751160136\) | \(-441510751160136\) | \([3]\) | \(11664\) | \(1.4969\) | |
1554.l1 | 1554n3 | \([1, 0, 0, -159177, -34893381]\) | \(-446030778735169043473/267461260498268466\) | \(-267461260498268466\) | \([]\) | \(34992\) | \(2.0462\) |
Rank
sage: E.rank()
The elliptic curves in class 1554n have rank \(1\).
Complex multiplication
The elliptic curves in class 1554n do not have complex multiplication.Modular form 1554.2.a.n
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.