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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3465h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3465.r2 | 3465h1 | \([0, 0, 1, -80463, -10287981]\) | \(-79028701534867456/16987307596875\) | \(-12383747238121875\) | \([]\) | \(48000\) | \(1.8091\) | \(\Gamma_0(N)\)-optimal |
| 3465.r1 | 3465h2 | \([0, 0, 1, -241113, 861529329]\) | \(-2126464142970105856/438611057788643355\) | \(-319747461127921005795\) | \([]\) | \(240000\) | \(2.6138\) |
Rank
sage: E.rank()
The elliptic curves in class 3465h have rank \(1\).
Complex multiplication
The elliptic curves in class 3465h do not have complex multiplication.Modular form 3465.2.a.h
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
