Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 77315f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77315.d2 | 77315f1 | \([0, 1, 1, -2945, -69236]\) | \(-262144/35\) | \(-377272536515\) | \([]\) | \(68172\) | \(0.95392\) | \(\Gamma_0(N)\)-optimal |
77315.d3 | 77315f2 | \([0, 1, 1, 19145, 180381]\) | \(71991296/42875\) | \(-462158857230875\) | \([]\) | \(204516\) | \(1.5032\) | |
77315.d1 | 77315f3 | \([0, 1, 1, -290115, 62820994]\) | \(-250523582464/13671875\) | \(-147372084576171875\) | \([]\) | \(613548\) | \(2.0525\) |
Rank
sage: E.rank()
The elliptic curves in class 77315f have rank \(0\).
Complex multiplication
The elliptic curves in class 77315f do not have complex multiplication.Modular form 77315.2.a.f
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.