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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 35280fr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.do7 | 35280fr1 | \([0, 0, 0, -147, -110446]\) | \(-1/15\) | \(-5269470474240\) | \([2]\) | \(49152\) | \(1.1200\) | \(\Gamma_0(N)\)-optimal |
| 35280.do6 | 35280fr2 | \([0, 0, 0, -35427, -2530654]\) | \(13997521/225\) | \(79042057113600\) | \([2, 2]\) | \(98304\) | \(1.4666\) | |
| 35280.do5 | 35280fr3 | \([0, 0, 0, -70707, 3346994]\) | \(111284641/50625\) | \(17784462850560000\) | \([2, 2]\) | \(196608\) | \(1.8131\) | |
| 35280.do4 | 35280fr4 | \([0, 0, 0, -564627, -163301614]\) | \(56667352321/15\) | \(5269470474240\) | \([2]\) | \(196608\) | \(1.8131\) | |
| 35280.do8 | 35280fr5 | \([0, 0, 0, 246813, 25128866]\) | \(4733169839/3515625\) | \(-1235032142400000000\) | \([2]\) | \(393216\) | \(2.1597\) | |
| 35280.do2 | 35280fr6 | \([0, 0, 0, -952707, 357734594]\) | \(272223782641/164025\) | \(57621659635814400\) | \([2, 2]\) | \(393216\) | \(2.1597\) | |
| 35280.do3 | 35280fr7 | \([0, 0, 0, -776307, 494303474]\) | \(-147281603041/215233605\) | \(-75611141774115655680\) | \([2]\) | \(786432\) | \(2.5063\) | |
| 35280.do1 | 35280fr8 | \([0, 0, 0, -15241107, 22901972114]\) | \(1114544804970241/405\) | \(142275702804480\) | \([2]\) | \(786432\) | \(2.5063\) |
Rank
sage: E.rank()
The elliptic curves in class 35280fr have rank \(1\).
Complex multiplication
The elliptic curves in class 35280fr do not have complex multiplication.Modular form 35280.2.a.fr
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
