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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1305.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1305.f1 | 1305g1 | \([1, -1, 0, -24, -37]\) | \(2146689/145\) | \(105705\) | \([2]\) | \(128\) | \(-0.28720\) | \(\Gamma_0(N)\)-optimal |
| 1305.f2 | 1305g2 | \([1, -1, 0, 21, -190]\) | \(1367631/21025\) | \(-15327225\) | \([2]\) | \(256\) | \(0.059378\) |
Rank
sage: E.rank()
The elliptic curves in class 1305.f have rank \(0\).
Complex multiplication
The elliptic curves in class 1305.f do not have complex multiplication.Modular form 1305.2.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.
