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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 13520w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13520.p2 | 13520w1 | \([0, 0, 0, -14027, -1042054]\) | \(-2609064081/2500000\) | \(-292464640000000\) | \([]\) | \(40320\) | \(1.4720\) | \(\Gamma_0(N)\)-optimal |
| 13520.p1 | 13520w2 | \([0, 0, 0, -1230827, 568122906]\) | \(-1762712152495281/171798691840\) | \(-20098017024582615040\) | \([]\) | \(282240\) | \(2.4449\) |
Rank
sage: E.rank()
The elliptic curves in class 13520w have rank \(1\).
Complex multiplication
The elliptic curves in class 13520w do not have complex multiplication.Modular form 13520.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
