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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 73920.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.a1 | 73920e4 | \([0, -1, 0, -8862721, -10152452639]\) | \(2349497892139423119368/8932840308315\) | \(292711311222865920\) | \([2]\) | \(3145728\) | \(2.5659\) | |
| 73920.a2 | 73920e3 | \([0, -1, 0, -1673441, 642377505]\) | \(15816313046221571528/3722207994264375\) | \(121969311556055040000\) | \([2]\) | \(3145728\) | \(2.5659\) | |
| 73920.a3 | 73920e2 | \([0, -1, 0, -562121, -153549879]\) | \(4795721641044996544/282532899951225\) | \(1157254758200217600\) | \([2, 2]\) | \(1572864\) | \(2.2193\) | |
| 73920.a4 | 73920e1 | \([0, -1, 0, 26124, -9900450]\) | \(30806768067763904/678292279285005\) | \(-43410705874240320\) | \([2]\) | \(786432\) | \(1.8727\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.a have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.a do not have complex multiplication.Modular form 73920.2.a.a
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.
