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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 39270s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39270.s3 | 39270s1 | \([1, 1, 0, -1985727, 1076200389]\) | \(865929782249693257251961/1598019506012160\) | \(1598019506012160\) | \([2]\) | \(774144\) | \(2.1736\) | \(\Gamma_0(N)\)-optimal |
| 39270.s2 | 39270s2 | \([1, 1, 0, -2006207, 1052840901]\) | \(892999621039369339714681/37160736124429209600\) | \(37160736124429209600\) | \([2, 2]\) | \(1548288\) | \(2.5202\) | |
| 39270.s4 | 39270s3 | \([1, 1, 0, 957313, 3901969029]\) | \(97025272885867934852999/6632160722964370440000\) | \(-6632160722964370440000\) | \([4]\) | \(3096576\) | \(2.8668\) | |
| 39270.s1 | 39270s4 | \([1, 1, 0, -5297407, -3290884859]\) | \(16440456162957329098383481/4841899901095142571840\) | \(4841899901095142571840\) | \([2]\) | \(3096576\) | \(2.8668\) |
Rank
sage: E.rank()
The elliptic curves in class 39270s have rank \(0\).
Complex multiplication
The elliptic curves in class 39270s do not have complex multiplication.Modular form 39270.2.a.s
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.
