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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 324870a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
324870.a1 | 324870a1 | \([1, 1, 0, -6785972148, -215127763537392]\) | \(293745816802769586284330715961/59069680920758324980800\) | \(6949488890646296175666139200\) | \([2]\) | \(542638080\) | \(4.3406\) | \(\Gamma_0(N)\)-optimal |
324870.a2 | 324870a2 | \([1, 1, 0, -6058237868, -263060855170728]\) | \(-209013547296432084489066845881/133140138457545234873585000\) | \(-15663804149391739337642401665000\) | \([2]\) | \(1085276160\) | \(4.6871\) |
Rank
sage: E.rank()
The elliptic curves in class 324870a have rank \(1\).
Complex multiplication
The elliptic curves in class 324870a do not have complex multiplication.Modular form 324870.2.a.a
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 Cremona 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 Cremona labels.