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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 375760q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 375760.q4 | 375760q1 | \([0, 0, 0, -5770187, 1083320954]\) | \(5187205194899938088481/2878078390139617280\) | \(11788609086011872378880\) | \([2]\) | \(26664960\) | \(2.9255\) | \(\Gamma_0(N)\)-optimal |
| 375760.q2 | 375760q2 | \([0, 0, 0, -69995467, 225062562426]\) | \(9259200968805149728839201/16008741033512550400\) | \(65571803273267406438400\) | \([2, 2]\) | \(53329920\) | \(3.2721\) | |
| 375760.q1 | 375760q3 | \([0, 0, 0, -1119462347, 14416583393914]\) | \(37878453234522762276932709921/113521496525360000\) | \(464984049767874560000\) | \([4]\) | \(106659840\) | \(3.6187\) | |
| 375760.q3 | 375760q4 | \([0, 0, 0, -48133067, 368213185146]\) | \(-3010886403566634803117601/12557142177117000158080\) | \(-51434054357471232647495680\) | \([2]\) | \(106659840\) | \(3.6187\) |
Rank
sage: E.rank()
The elliptic curves in class 375760q have rank \(0\).
Complex multiplication
The elliptic curves in class 375760q do not have complex multiplication.Modular form 375760.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
