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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5915.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5915.g1 | 5915a3 | \([1, -1, 0, -67040, -6343349]\) | \(6903498885921/374712065\) | \(1808663567750585\) | \([2]\) | \(21504\) | \(1.6836\) | |
| 5915.g2 | 5915a2 | \([1, -1, 0, -12115, 390456]\) | \(40743095121/10144225\) | \(48964236528025\) | \([2, 2]\) | \(10752\) | \(1.3370\) | |
| 5915.g3 | 5915a1 | \([1, -1, 0, -11270, 463295]\) | \(32798729601/3185\) | \(15373386665\) | \([2]\) | \(5376\) | \(0.99046\) | \(\Gamma_0(N)\)-optimal |
| 5915.g4 | 5915a4 | \([1, -1, 0, 29290, 2452425]\) | \(575722725759/874680625\) | \(-4221916312875625\) | \([2]\) | \(21504\) | \(1.6836\) |
Rank
sage: E.rank()
The elliptic curves in class 5915.g have rank \(0\).
Complex multiplication
The elliptic curves in class 5915.g do not have complex multiplication.Modular form 5915.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
