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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 346560.fl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.fl1 | 346560fl8 | \([0, -1, 0, -123225665, -526460735775]\) | \(16778985534208729/81000\) | \(998956429737984000\) | \([2]\) | \(31850496\) | \(3.0761\) | |
| 346560.fl2 | 346560fl7 | \([0, -1, 0, -10478145, -1773331743]\) | \(10316097499609/5859375000\) | \(72262473216000000000000\) | \([2]\) | \(31850496\) | \(3.0761\) | |
| 346560.fl3 | 346560fl6 | \([0, -1, 0, -7705665, -8214911775]\) | \(4102915888729/9000000\) | \(110995158859776000000\) | \([2, 2]\) | \(15925248\) | \(2.7295\) | |
| 346560.fl4 | 346560fl4 | \([0, -1, 0, -6665985, 6626520225]\) | \(2656166199049/33750\) | \(416231845724160000\) | \([2]\) | \(10616832\) | \(2.5268\) | |
| 346560.fl5 | 346560fl5 | \([0, -1, 0, -1583105, -659834463]\) | \(35578826569/5314410\) | \(65541531355109130240\) | \([2]\) | \(10616832\) | \(2.5268\) | |
| 346560.fl6 | 346560fl2 | \([0, -1, 0, -427905, 97745697]\) | \(702595369/72900\) | \(899060786764185600\) | \([2, 2]\) | \(5308416\) | \(2.1802\) | |
| 346560.fl7 | 346560fl3 | \([0, -1, 0, -312385, -219818783]\) | \(-273359449/1536000\) | \(-18943173778735104000\) | \([2]\) | \(7962624\) | \(2.3830\) | |
| 346560.fl8 | 346560fl1 | \([0, -1, 0, 34175, 7455265]\) | \(357911/2160\) | \(-26638838126346240\) | \([2]\) | \(2654208\) | \(1.8337\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.fl have rank \(0\).
Complex multiplication
The elliptic curves in class 346560.fl do not have complex multiplication.Modular form 346560.2.a.fl
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
