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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 155298p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155298.x2 | 155298p1 | \([1, 1, 1, -867, -14079]\) | \(-72079590632113/39577384704\) | \(-39577384704\) | \([2]\) | \(238592\) | \(0.73704\) | \(\Gamma_0(N)\)-optimal |
155298.x1 | 155298p2 | \([1, 1, 1, -15347, -738079]\) | \(399756892180585393/64490911056\) | \(64490911056\) | \([2]\) | \(477184\) | \(1.0836\) |
Rank
sage: E.rank()
The elliptic curves in class 155298p have rank \(0\).
Complex multiplication
The elliptic curves in class 155298p do not have complex multiplication.Modular form 155298.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.