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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 101150l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101150.j1 | 101150l1 | \([1, 1, 0, -50725, 4377125]\) | \(-11060825617/2744\) | \(-3580962875000\) | \([]\) | \(326592\) | \(1.3965\) | \(\Gamma_0(N)\)-optimal |
101150.j2 | 101150l2 | \([1, 1, 0, 21525, 15575875]\) | \(845095823/80707214\) | \(-105324175320218750\) | \([]\) | \(979776\) | \(1.9458\) |
Rank
sage: E.rank()
The elliptic curves in class 101150l have rank \(0\).
Complex multiplication
The elliptic curves in class 101150l do not have complex multiplication.Modular form 101150.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.