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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 348480.fr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.fr1 | 348480fr2 | \([0, 0, 0, -15708, -758032]\) | \(-296587984/125\) | \(-180652032000\) | \([]\) | \(414720\) | \(1.1211\) | |
| 348480.fr2 | 348480fr1 | \([0, 0, 0, 132, -4048]\) | \(176/5\) | \(-7226081280\) | \([]\) | \(138240\) | \(0.57182\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 348480.fr have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.fr do not have complex multiplication.Modular form 348480.2.a.fr
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
