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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 101150p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101150.v1 | 101150p1 | \([1, -1, 0, -5488742, 4676916916]\) | \(9869198625/614656\) | \(1138917965877188000000\) | \([2]\) | \(5013504\) | \(2.7918\) | \(\Gamma_0(N)\)-optimal |
101150.v2 | 101150p2 | \([1, -1, 0, 4337258, 19582958916]\) | \(4869777375/92236816\) | \(-170908877254445524250000\) | \([2]\) | \(10027008\) | \(3.1384\) |
Rank
sage: E.rank()
The elliptic curves in class 101150p have rank \(0\).
Complex multiplication
The elliptic curves in class 101150p do not have complex multiplication.Modular form 101150.2.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.