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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 294525x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 294525.x3 | 294525x1 | \([1, -1, 1, -30105455, -63571685578]\) | \(264918160154242157473/536027170833\) | \(6105684492769640625\) | \([2]\) | \(11796480\) | \(2.8556\) | \(\Gamma_0(N)\)-optimal |
| 294525.x2 | 294525x2 | \([1, -1, 1, -30430580, -62128130578]\) | \(273594167224805799793/11903648120953281\) | \(135589991877733466390625\) | \([2, 2]\) | \(23592960\) | \(3.2022\) | |
| 294525.x1 | 294525x3 | \([1, -1, 1, -81551705, 201350147672]\) | \(5265932508006615127873/1510137598013239041\) | \(17201411077369550951390625\) | \([2]\) | \(47185920\) | \(3.5487\) | |
| 294525.x4 | 294525x4 | \([1, -1, 1, 15488545, -233222790328]\) | \(36075142039228937567/2083708275110728497\) | \(-23734739571183141786140625\) | \([2]\) | \(47185920\) | \(3.5487\) |
Rank
sage: E.rank()
The elliptic curves in class 294525x have rank \(0\).
Complex multiplication
The elliptic curves in class 294525x do not have complex multiplication.Modular form 294525.2.a.x
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.
