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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 115920.et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.et1 | 115920bt4 | \([0, 0, 0, -30987, 2099466]\) | \(4407931365156/100625\) | \(75116160000\) | \([2]\) | \(163840\) | \(1.2004\) | |
| 115920.et2 | 115920bt3 | \([0, 0, 0, -8307, -260766]\) | \(84923690436/9794435\) | \(7311506549760\) | \([2]\) | \(163840\) | \(1.2004\) | |
| 115920.et3 | 115920bt2 | \([0, 0, 0, -2007, 30294]\) | \(4790692944/648025\) | \(120937017600\) | \([2, 2]\) | \(81920\) | \(0.85380\) | |
| 115920.et4 | 115920bt1 | \([0, 0, 0, 198, 2511]\) | \(73598976/276115\) | \(-3220605360\) | \([2]\) | \(40960\) | \(0.50723\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.et have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.et do not have complex multiplication.Modular form 115920.2.a.et
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.
