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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 29575.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29575.f1 | 29575w2 | \([0, 1, 1, -626708, 191710744]\) | \(-2887553024/16807\) | \(-158445661841796875\) | \([]\) | \(468000\) | \(2.1414\) | |
| 29575.f2 | 29575w1 | \([0, 1, 1, 7042, -315506]\) | \(4096/7\) | \(-65991529296875\) | \([]\) | \(93600\) | \(1.3367\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29575.f have rank \(1\).
Complex multiplication
The elliptic curves in class 29575.f do not have complex multiplication.Modular form 29575.2.a.f
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 LMFDB 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 LMFDB labels.
