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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 151838g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 151838.a3 | 151838g1 | \([1, 1, 0, -44706, -3656888]\) | \(11134383337/316\) | \(280451163196\) | \([]\) | \(403200\) | \(1.2982\) | \(\Gamma_0(N)\)-optimal |
| 151838.a2 | 151838g2 | \([1, 1, 0, -78341, 2498317]\) | \(59914169497/31554496\) | \(28004731352099776\) | \([]\) | \(1209600\) | \(1.8475\) | |
| 151838.a1 | 151838g3 | \([1, 1, 0, -5013076, 4318113872]\) | \(15698803397448457/20709376\) | \(18379647431213056\) | \([]\) | \(3628800\) | \(2.3969\) |
Rank
sage: E.rank()
The elliptic curves in class 151838g have rank \(2\).
Complex multiplication
The elliptic curves in class 151838g do not have complex multiplication.Modular form 151838.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
