Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 304b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304.c2 | 304b1 | \([0, -1, 0, -248, -1424]\) | \(-413493625/152\) | \(-622592\) | \([]\) | \(48\) | \(0.079705\) | \(\Gamma_0(N)\)-optimal |
| 304.c3 | 304b2 | \([0, -1, 0, 152, -5776]\) | \(94196375/3511808\) | \(-14384365568\) | \([]\) | \(144\) | \(0.62901\) | |
| 304.c1 | 304b3 | \([0, -1, 0, -1368, 157168]\) | \(-69173457625/2550136832\) | \(-10445360463872\) | \([]\) | \(432\) | \(1.1783\) |
Rank
sage: E.rank()
The elliptic curves in class 304b have rank \(0\).
Complex multiplication
The elliptic curves in class 304b do not have complex multiplication.Modular form 304.2.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 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.
