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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 30015.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30015.b1 | 30015f4 | \([1, -1, 1, -49838, -4269774]\) | \(18778886261717401/732035835\) | \(533654123715\) | \([2]\) | \(61440\) | \(1.3346\) | |
| 30015.b2 | 30015f3 | \([1, -1, 1, -15008, 654702]\) | \(512787603508921/45649063125\) | \(33278167018125\) | \([2]\) | \(61440\) | \(1.3346\) | |
| 30015.b3 | 30015f2 | \([1, -1, 1, -3263, -59394]\) | \(5268932332201/900900225\) | \(656756264025\) | \([2, 2]\) | \(30720\) | \(0.98804\) | |
| 30015.b4 | 30015f1 | \([1, -1, 1, 382, -5448]\) | \(8477185319/21880935\) | \(-15951201615\) | \([2]\) | \(15360\) | \(0.64147\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30015.b have rank \(1\).
Complex multiplication
The elliptic curves in class 30015.b do not have complex multiplication.Modular form 30015.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
