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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 68544cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68544.h1 | 68544cv1 | \([0, 0, 0, -10764, -430064]\) | \(-19486825371/11662\) | \(-82542329856\) | \([]\) | \(92160\) | \(1.0387\) | \(\Gamma_0(N)\)-optimal |
| 68544.h2 | 68544cv2 | \([0, 0, 0, 9396, -1778544]\) | \(17779581/275128\) | \(-1419600048685056\) | \([]\) | \(276480\) | \(1.5880\) |
Rank
sage: E.rank()
The elliptic curves in class 68544cv have rank \(0\).
Complex multiplication
The elliptic curves in class 68544cv do not have complex multiplication.Modular form 68544.2.a.cv
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
