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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 30492c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30492.bg2 | 30492c1 | \([0, 0, 0, 4719, 30613]\) | \(15185664/9317\) | \(-7130433817584\) | \([]\) | \(69120\) | \(1.1555\) | \(\Gamma_0(N)\)-optimal |
| 30492.bg1 | 30492c2 | \([0, 0, 0, -75141, 8229573]\) | \(-84098304/3773\) | \(-2105010135519984\) | \([]\) | \(207360\) | \(1.7048\) |
Rank
sage: E.rank()
The elliptic curves in class 30492c have rank \(1\).
Complex multiplication
The elliptic curves in class 30492c do not have complex multiplication.Modular form 30492.2.a.c
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.
