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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 81120l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81120.z3 | 81120l1 | \([0, -1, 0, -38250, 2835000]\) | \(20034997696/455625\) | \(140749750440000\) | \([2, 2]\) | \(368640\) | \(1.5015\) | \(\Gamma_0(N)\)-optimal |
81120.z4 | 81120l2 | \([0, -1, 0, 4000, 8716200]\) | \(2863288/13286025\) | \(-32834101782643200\) | \([2]\) | \(737280\) | \(1.8481\) | |
81120.z2 | 81120l3 | \([0, -1, 0, -83880, -5177628]\) | \(26410345352/10546875\) | \(26064768600000000\) | \([2]\) | \(737280\) | \(1.8481\) | |
81120.z1 | 81120l4 | \([0, -1, 0, -608625, 182959425]\) | \(1261112198464/675\) | \(13345161523200\) | \([2]\) | \(737280\) | \(1.8481\) |
Rank
sage: E.rank()
The elliptic curves in class 81120l have rank \(0\).
Complex multiplication
The elliptic curves in class 81120l do not have complex multiplication.Modular form 81120.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.