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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 485100q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 485100.q1 | 485100q1 | \([0, 0, 0, -11172000, -11847434375]\) | \(57537462272/10673289\) | \(28606456120061531250000\) | \([2]\) | \(35389440\) | \(3.0272\) | \(\Gamma_0(N)\)-optimal |
| 485100.q2 | 485100q2 | \([0, 0, 0, 22178625, -69043756250]\) | \(28134667888/64304361\) | \(-2757567803176840500000000\) | \([2]\) | \(70778880\) | \(3.3738\) |
Rank
sage: E.rank()
The elliptic curves in class 485100q have rank \(1\).
Complex multiplication
The elliptic curves in class 485100q do not have complex multiplication.Modular form 485100.2.a.q
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.
