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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 17325bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17325.c2 | 17325bl1 | \([0, 0, 1, -7827825, 8429654506]\) | \(116423188793017446400/91315917\) | \(41605814683125\) | \([]\) | \(422400\) | \(2.3533\) | \(\Gamma_0(N)\)-optimal |
| 17325.c1 | 17325bl2 | \([0, 0, 1, -15198375, -9755843594]\) | \(1363413585016606720/644626239703677\) | \(183567394040617395703125\) | \([]\) | \(2112000\) | \(3.1580\) |
Rank
sage: E.rank()
The elliptic curves in class 17325bl have rank \(1\).
Complex multiplication
The elliptic curves in class 17325bl do not have complex multiplication.Modular form 17325.2.a.bl
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.
