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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 13475j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13475.v3 | 13475j1 | \([0, -1, 1, -408, -7407]\) | \(-4096/11\) | \(-20220921875\) | \([]\) | \(10080\) | \(0.66495\) | \(\Gamma_0(N)\)-optimal |
| 13475.v2 | 13475j2 | \([0, -1, 1, -12658, 997093]\) | \(-122023936/161051\) | \(-296054517171875\) | \([]\) | \(50400\) | \(1.4697\) | |
| 13475.v1 | 13475j3 | \([0, -1, 1, -9579908, 11415939093]\) | \(-52893159101157376/11\) | \(-20220921875\) | \([]\) | \(252000\) | \(2.2744\) |
Rank
sage: E.rank()
The elliptic curves in class 13475j have rank \(1\).
Complex multiplication
The elliptic curves in class 13475j do not have complex multiplication.Modular form 13475.2.a.j
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
