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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 123840.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.t1 | 123840e2 | \([0, 0, 0, -30348, -2017872]\) | \(4792616856/46225\) | \(29813855846400\) | \([2]\) | \(294912\) | \(1.4054\) | |
| 123840.t2 | 123840e1 | \([0, 0, 0, -3348, 23328]\) | \(51478848/26875\) | \(2166704640000\) | \([2]\) | \(147456\) | \(1.0588\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 123840.t have rank \(1\).
Complex multiplication
The elliptic curves in class 123840.t do not have complex multiplication.Modular form 123840.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
