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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 141960.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141960.s1 | 141960p3 | \([0, -1, 0, -145565840, 675951010812]\) | \(69014771940559650916/9797607421875\) | \(48426167994750000000000\) | \([4]\) | \(30965760\) | \(3.3689\) | |
| 141960.s2 | 141960p4 | \([0, -1, 0, -59355560, -169284312900]\) | \(4678944235881273796/202428825314625\) | \(1000535322509373216384000\) | \([2]\) | \(30965760\) | \(3.3689\) | |
| 141960.s3 | 141960p2 | \([0, -1, 0, -9923060, 8534276100]\) | \(87450143958975184/25164018140625\) | \(31094248764756996000000\) | \([2, 2]\) | \(15482880\) | \(3.0223\) | |
| 141960.s4 | 141960p1 | \([0, -1, 0, 1644145, 881413272]\) | \(6364491337435136/8034291412875\) | \(-620479841604604254000\) | \([2]\) | \(7741440\) | \(2.6758\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141960.s have rank \(1\).
Complex multiplication
The elliptic curves in class 141960.s do not have complex multiplication.Modular form 141960.2.a.s
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
