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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 303450.fm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.fm1 | 303450fm2 | \([1, 1, 1, -858537888688, -306187749014132719]\) | \(37769548376817211811066153/1011738331054080\) | \(1874685941411283419811840000000\) | \([2]\) | \(3609722880\) | \(5.3224\) | |
303450.fm2 | 303450fm1 | \([1, 1, 1, -53591968688, -4796677864052719]\) | \(-9186763300983704416553/47730830553907200\) | \(-88442153731655955224985600000000\) | \([2]\) | \(1804861440\) | \(4.9758\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.fm have rank \(1\).
Complex multiplication
The elliptic curves in class 303450.fm do not have complex multiplication.Modular form 303450.2.a.fm
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.