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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 10304.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10304.f1 | 10304e2 | \([0, 1, 0, -1953, 32575]\) | \(12576878500/1127\) | \(73859072\) | \([2]\) | \(5120\) | \(0.54982\) | |
| 10304.f2 | 10304e1 | \([0, 1, 0, -113, 559]\) | \(-9826000/3703\) | \(-60669952\) | \([2]\) | \(2560\) | \(0.20324\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10304.f have rank \(2\).
Complex multiplication
The elliptic curves in class 10304.f do not have complex multiplication.Modular form 10304.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
