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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 302549.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302549.b1 | 302549b1 | \([1, 1, 1, -81484, 8917852]\) | \(23320116793/2873\) | \(7371331973057\) | \([2]\) | \(1244160\) | \(1.4924\) | \(\Gamma_0(N)\)-optimal |
| 302549.b2 | 302549b2 | \([1, 1, 1, -74639, 10486726]\) | \(-17923019113/8254129\) | \(-21177836758592761\) | \([2]\) | \(2488320\) | \(1.8390\) |
Rank
sage: E.rank()
The elliptic curves in class 302549.b have rank \(2\).
Complex multiplication
The elliptic curves in class 302549.b do not have complex multiplication.Modular form 302549.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
