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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 155232x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155232.be3 | 155232x1 | \([0, 0, 0, -15141, -624260]\) | \(69934528/9801\) | \(53798000122944\) | \([2, 2]\) | \(393216\) | \(1.3609\) | \(\Gamma_0(N)\)-optimal |
155232.be2 | 155232x2 | \([0, 0, 0, -63651, 5555914]\) | \(649461896/72171\) | \(3169191279969792\) | \([2]\) | \(786432\) | \(1.7075\) | |
155232.be4 | 155232x3 | \([0, 0, 0, 24549, -3346994]\) | \(37259704/131769\) | \(-5786273791001088\) | \([2]\) | \(786432\) | \(1.7075\) | |
155232.be1 | 155232x4 | \([0, 0, 0, -233436, -43410080]\) | \(4004529472/99\) | \(34778505129984\) | \([2]\) | \(786432\) | \(1.7075\) |
Rank
sage: E.rank()
The elliptic curves in class 155232x have rank \(0\).
Complex multiplication
The elliptic curves in class 155232x do not have complex multiplication.Modular form 155232.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.